The problems of philosophy

lOME UNIVERSITY LIBRARY
OF MODERN KNOWLEDGE

No. 35

™^"»s». xivv

Editors:

HERBERT FISHER, M.A., F.B.A.
Prof. GILBERT MURRAY, Litt.D,,

LL.D., F.B.A.
Prof. J. ARTHUR THOMSON, M.A.
Prof. WiLLIAM T. BREWSTER, M.A.

THE HOME UlTIVEESITY LIBKAEY

OF MODEEIST KITOWLEDGE

i6mo cloth, so cents net, by mail 56 cents

PHILOSOPHY AND RELIGIONi

Just Published
PROBLEMS OF PHILOSOPHY . By Bebtrand RussEii;

BUDDHISM By Mrs. Rhys Davids

ENGLISH SECTS By W. B. Selbib

THE MAKING OF THE NEW

TESTAMENT . By B. W. Bacon

ETHICS By G. E. Mooke

MISSIONS By Mrs. Creighton

Future Issues

THE OLD TESTAMENT .... By George Moore
BETWEEN THE OLD AND NEW

TESTAMENTS By R. H. Charles

COMPARATIVE RELIGION . . By J. Estlin CARPENTSa
A HISTORY OF FREEDOM OF

THOUGHT . . . . . . . >: .. . By J. B. Buby

THE PROBLEMS
OF PHILOSOPHY

I

BY

BERTRAND RUSSELL

M.A.. v.R.S,

LECTURER AND LATE Fi:LLOW OF TRINITY COLLEGE
CAMBRIDGE

•C^

NEW YORK
HENRY HOLT AND COMPANY

LONDON
WTLLIAMS AND NORGATE

PREFACE

In the following pages, I have confined
myself in the main to those problems of
philosophy in regard to which it seemed to
me possible to say something positive and-^
constructive, since merely negative criticism
seemed out of place. For this reason, theory
of knowledge occupies a larger space than
metaphysics in the present volume, and some
topics much discussed by philosophers are
treated very briefly, if at all.

I have derived valuable assistance from
unpublished writings of Mr. G. E. Moore and •''
Mr. J. M. Keynes : from the former, as re-
gards the relations of sense-data to physical
objects, and from the latter as regards prob-
ability and induction. I have also profited
greatly by the criticisms and suggestions of
Professor Gilbert Murray.

CONTENTS

^Kii 1

piaig
I APPEARANCE AND REALITY , . 9

II THE EXISTENCE OF MATTER , . 26
ni THE NATURE OF MATTER ... 42
^ IV IDEALISM 68

V KNOWLEDGE BY ACQUAINTANCE AND

KNOWLEDGE BY DESCRIPTION . . 72

VI ON INDUCTION ..... 93

VII ON OUR KNOWLEDGE OF GENERAL

PRINCIPLES . . . . . 109

VIII HOW A PRIORI KNOWLEDGE IS POSSIBLE 127

IX THE WORLD OF UNI VERS ALS . .142

X ON OUR KNOWLEDGE OF UNIVERSALS . 168

XI ON INTUITIVE KNOWLEDGE . . .174

vii

viii CONTENTS

OHAPTBB PA.QH

XII TRUTH AND FALSEHOOD . . .186

XIII KNOWLEDGE, ERROR, AND PROBABLE

OPINION 204

XIV THE LIMITS OF PHILOSOPHICAL KNOW-

LEDGE 220

XV THE VALUE OF PHILOSOPHY . . 237

BIBLIOGRAPHICAL NOTE . . . 251

INDEX 253

THE
PROBLEMS OF PHILOSOPHY

CHAPTER I

APPEARANCE AND REALITY

IsJhei:gjany_knowledge inthe world which . .
is so certain that no reasonable man could^
doubt it ? This question, which at first sight
might not seem difficult, is really one of the
most difficult that can be asked. When we
have realised the obstacles in the way of a
straightforward and confident answer, we
shall be well launched on the study of philo-
sophy— for philosophy is merely the attempt
to answer such ultimate questions, not
carelessly and dogmatically, as we do in
ordinary life and even in the sciences, but
critically, after exploring all that makes such
9

10 THE PROBLEMS OF PHILOSOPHY

questions puzzling, and after realisiiig all
the vagueness and confusion that underlie
our ordinary ideas.

In daily life, we assume as certain many
things which, on a closer scrutiny, are found
to be so full of apparent contradictions that
only a great amount of thought enables us
to know what it is that we really may believe.

In the seari^h ^^^ ^^^^^^r^^YilJJ:J^J]!^!^Iirf^^ ^^
I^Arfjn ^^ifV^ r>nr preseij^t cxperiences^ ond In
gr>r^P ^"^rii^ea T^^ dftliht, knowlpdgp is t,^ be
jdexivfid^-frflaaajliem. But any statement as
to what it is that our immediate experiences
make us know is very likely to be wrong. It
seems to me that I am now sitting in a chair,
at a table of a certain shape, on which I see
sheets of paper with writing or print. By
turning my head I see out of the window
buildings and clouds and the sun. I believe
that the sun is about ninety-three million miles
from the earth ; that it is a hot globe many
times bigger than the earth ; that, owing to
the earth's rotation, it rises every morning,
and will continue to do so for an indefinite
time in the future. I believe that,^ if any

APPEARANCE AND REALITY H

other normal person comes into my ropm, he "^
IfviJl see the same chairs and tables and books "^^
and papers as I see, and that the table which

Ksee is the same as the table which I feel
iressing against my arm. All this seems to
e so evident as to be hardly worth stating,
xcept in answer to a man who doubts
v/hether I know anything. Yet all this may
be reasonably doubted, and all of it requires
much careful discussion before we can be
sure that we have stated it in a form that is
wholly true.

t To make our difficulties plain, let us con-
centrate attention on the table. To the eye
p it is oblong, brown and shiny, to the touch
it is smooth and cool and hard ; when I
tap it, it gives out a wooden sound. Any one
else who sees and feels and hears the table
will agree with this description, so that it
might seem as if no difficjiltj^ would arise ;
but as_sogn^s we^try to be more precise our
troujblesJaegin. Although I believe that the
table is " really " of the same colour all over,
the parts that reflect the light look much
brighter than the other parts, and some

12 THE PROBLEMS OF PHILOSOPHY

parts look white because of reflected light.
I know that, if I move, the parts that re-*
fleet the light will be different, so that the
apparent distribution of colours on the table
will change. It follows that if several people
are looking at the table at the same moment,
no two of them will see exactly the same
distribution of colours, because no two
can see it from exactly the same point of
view, and any change in the point of view
makes some change in the way the light is
reflected.

For most_BTaciiiial..purpGses these differ-
ences are unimportant, but to the painter
they are all-important : the painter has to
unlearn the habit of thinking that things
seem to have the colour which common se^nse
says they "reajly" have, and to learn the
habit of seeing things as they appear^ Here
we have already the beginning csf one of
the distinctions that cause most trouble in
philosophy — the . -Ji.llinctjon Jbetween ,. .'lap-
pearance '^ and " reality," between^whaT
things seem to be aiid what they are. The
pamter wailtS^to know what fliings**seem to

]

APPEARANCE AND REALITY 13

be, the practical man and the philosopher
want to know whftt theyf'are;^'but the philo-
sopher's wish to know this is stronger than
the practical man's, and is more troubled by-
knowledge as to the difficulties of answering
the question.

To return to the table. It is evident from
what we have found, that there is no colour
which pre-eminently appears to be the colour
of the table, or even of any one particular
part of the table — it appears to be of different

j colours from different points of view, and
there is no reason for regarding some of
these as more really its colour than others.
And we know that even from a given point
of view the colour will seem different by

' -Q^tificial light, or to a colour-blind man, or
to a man wearing blue spectacles, wMle in
the dark there will be no colour at all, though
to touch and hearing the table will be un-
changed. Thus colour is nLQJLSjamething which
isinherenLofi^the table, but something de-
pending upon the tafile and the spectator
and the way the light falls on the table.
When, in ordmury lifej wej£eak of the colour

14 THE PROBLEMS OF PHILOSOPHY

of the table, we only mean the sort of colour
which it will seem to have to a normal
spectator from an ordinary point of view
under usual conditions of light. But the
other colours which appear under other
conditions have just as good a right to be
considered real ; and therefore, to avoid
i favouritism, we are compelled to deny that,
in itself, the table has any one particular
' ' colour.

-The^same thing applies to the-^texture.

With the naked eye one can see the grain,

but otherwise the table looks smooth and

even. If we look at it through a microscope,

we should see roughnesses and hills and

valleys, and all sorts of differences that are

I imperceptible to the naked eye. Which of

\\ these is the " reay table ? We are~imtua.

\\ rally tempted to say that what we see

l\ through the microscope is more real, but

\ihat in turn would Jtne^-i^h^^ still

mtH*e- powerf ul__mi(grDscope. '^"^J^'^iien^" we

'--'''cannoFjrust what we see v^Mti the naked

'< — ^it^a- wiiy should we trust what we see

^through a microscope ? Thus, again, the

APPEARANCE AND REALITY 15

confidence in our senses with which we be-
gan deserts us.

The .g^gge cj theJ^ablei^jaaJ^ter^^We
are all in the habit of judging as to the
" real " shapes of things, and we do this so
unreflectingly that we come to think we
actually see the real shapes. But, in fact,
as we all have to learn if we try to draw, a
given thing looks different in shape from
every different point of view. If our table
is *' really '- rectangular, it will look^lrom"
almost alLpLOiiiis^f" view,"" as if 'ilrliaa- f wo
acute angles and two obtuse angles. If
opposite sides are parallel, they will look as
if they converged to a point away from the
spectator ; if they are of equal length,, .they
will look as if the nearer side were longer.
All these things are not commonly noticed
in looking at a table^ because experience has
taught us to jsonstruct the "real" shape fcom
the anpn rpnt. gh n pf>. and the *' real " shape <
is what interests us as practical men. But
tteJ.l?^L'' ^tep?_ js not what \ye see ; it is \
something. J|if erred from what ^we^ see. And s
wharwe see is constantly changing in shape

/

;>

^

16 THE PROBLEMS OF PHILOSOPHY

as we move about the room ; so that here
again the s^ses seem not to give us the truth
about the tabla . itself ,but_ Quly , ^bout-ihe
_jappearance of the table.

SirniTaF"difficultres arise when we consider
the sense of touch. It is true that the table
always gives us a ^sensation of hardness, and
we feel that it resists pressure. But the
isensation we obtain depends upon how har^
we press the table and also upon what partj
of the body we press with ; thus the various^
' sensations due to various pressures or variolas
parts of the body cannot be supposed to-
re veal directly any definite property of the ^
table, but at most to be si^ns of sornje^
property which perhaps causes'^all the s^i:^
sations, but is not actually apparent in any/
of them. And the same applies still more
obviously to the sounds which can be elicited
by rapping the table. *

/ TJfeus it becomes evident that thejreal table,
J ^f fh^e is one, is not the same as what we
imiae'diate^y e^^enence^ by sight or touch or
hearing. The real table, if there is one, is
\ V ijtot immediately known to us at all, but must

\-

APPEARANCE AND REALITY 17

be an inference from what is immediately \
known, llenee, two v-ery difficult questions
atlSnce aif?se> jiamely , |j.\lg there a real table >
I at all ? f t^^ so, what sort of object can it 1

It will help us in considering these questions
to have a few^simple terms of which the j\
meaning is definite and clear. Let us give \
Uhe name of " sense.-^g-tg, " to the things tha,fc. j ,]
arft^ nngj^ediately known in sensation: such
things as colours, sounds, smells, hardnesses,
roughnesses, and so on. We shall give the
name " sensation " to the experience of ?
being immediately aware of these things, i
Thus, whenever we see a colour, we have a |
sensation of the colour, but the colour itself l
is a sense-datum, not a sensation. The
colour is that of which we are immediately
aware, and the awareness itself is the sensation.
It is plainJJaat tf we-are^to know anything
abQut_t^he table, it^piust be by means of the
sense-data— brawn.,., colour, oblong shape,
smoothness;" ^Tc.—wEich we assocfate -oyith
the- table j~ but for-the Teasonirwhich, have
jcn given, wecannot say that the table is the*

18 THE PROBLEMS OF PHILOSOPHY

sense-data, or even that the sense-data are
directly properties ^ of the table. Thus ai^
problem arists as to the relation of the sense-
-data to the real table, supposing .there is
such «, thing. -

,./ThfiL;reiil table, jLifc. exists, we will call a

! "physical object." Thus we have to consider

the relation pi sense-data to physical objects.

The collection of all physical objects is called

. "matte;'." Thus our two questions may

I i "^'be re-stated as follows : (1) Is there any

^1 J f such thing as matter ? (2) If so, what is its

"^^4 nature ?

, ,^,/ The philosopher who first brought pro-

minently forward the reasStts foj*. regarding

T^^fiie immediate_oBjeTt^^ senses as not

\ existing in3ependently of us was Bishop

^Berkeley (1685-1753). His Three Dialogues

"between Tlylas and Philonous, in Opposition.

to Sceptics and Atheists, undertake to prove

t^hat there is no such, thing as matter. at all.

and that the world consists of nothing but

nunds.ajxd. their idej3.s. Hylas has hitherto

believed in matter, but he is no match for

Philonous, who mercilessly drives him into

H

i| APPEARANCE AND REALITY 19

contradictions and paradoxes, and makes
his own denial of matter seem, in the end,
as if it were almost common sense. The
arguments employed are of very different
value: some are important and sound,
others are confused or quibbling. But

Berkeley retains the merit of having shown i

II -— — .,.1, ,^,, ^ f

4iat Jthe existence dt'matter'ls^ enable of .'
being denied" without absurdity, and^that if

^liefe are any things that exist independcni&y" ; T '
of^usjbhey cannot be the immediate objecta// ^ "^

of our sensations.- "^- ---. \ t «

There are two different questions involved
when we ask whether matter exists, and it is
important to keep them clear. W,acommonly
mean by " matter '' something which "'is""
opposed:^ T6"*^*lnind," something which we
tlunk-ef-as ucuupying space and as radically

,jnc^able-©l-anyS5rl 61 thought or conscious-]
ness^.^-it is chiefly in this sense that Berkeley \
denies matter ; that is to say, he does not •
deny that the sense-data which we commonly
take as signs of the existence of the table are
really signs of the existence of something inde-
pendent of us, but he does deny that this some-

i

20 THE PROBLEMS OF PHILOSOPHY

thing isCnon-mental,- thatdt.isLJaeither mind,
nor ideas entertained by some mind. Hel
admits that there must be something which
continues to exist when we go out of the roomj
or shut our eyes, and that what we calj
seeing the table does really give us reason
for believing in something which persists
even when we are not seeing it. But hfe
thinks that this something cannot be radi-
cally different in nature from what we see, and
cannot be independent of seeing altogether,
though it must be independent of our seeing.
He is thus led to regard the *' real " table as
an idea in the mind of God. Such an idea
has the required permanence and independence
of ourselves, without being — as matter would
otherwise be — something quite unknowable,
in the sense that we can only infer it, and
can never be directly and immediately aware
of it.

Otfeer-pMosepligrs since Berkeley have
also held that, although the t^^^a.do^s ,not
depend for its existence upon being seen by
me,'"'Tr";3Sprndepeiid upon bmng 'seen (or
otherwise apprehended in sensation) hy some

APPEARANCE AND REALITY 21

mind — not necessarily the mind of God,
but mSre often the whole collective mind of
jthe imiverse. This they hold, as Berkeley

7tees~ chiefly because they think there can
be nothing real — or at any rate nothing
known to be real — except minds and their
thoughts and feelings. We might state the
argument by which they support their view
in some such way as this : " Whatever
can be thought of is an ~iHea Tn the

XTmird~^©f'-4h©-^rson thinking of it. ; tberef ore

— »o%h«ig^cah be thought of except ideas in
minds ; therefore anything else is incon-

^j^pivabl^ -«ft4'-*wli:;i ^ is^ ineoncei vable cannot
exist."

Sucli^ 311 argument, in my opinion, is
iallaciqus ; and of course those who advance
it do not put it so shortly or so crudely. But
whether valid or not, the argument has been
very widely advanced in one form or another ;
and very many philosophers, perhaps a
majority, have held that there is nothing real
except minds and their ideas. Such philo-
sophers are called *' idealists." When they
me lo explaining matter, they either say.

22 THE PROBLEMS OF PHILOSOPH^

like Berkeley, that matter is really nothing^
but a collection of ideas, or they say, like,
III Leibniz (1646-1716), that what appear^ a^
11 matter is really a collection of more or less
rudimentary minds.

But these philosophers, though they deny
matter as opposed to mind, nevertheless, in
another sense, admit matter. It will be
remembered that we asked two questions ;
namely, (1) Is there a real table at all ? (2KIf
so, what sort of object can it be ? NdV
both Berkeley, and Leibniz admit that th^i'e^
is SL real table, but Berkeley says it is certain
ideas in the mind of God, and Leibniz sSjS^
it is a colony of souls. Thus both of theiriK
answer our first question in the affirmgtfive,
and only diverge from the views' of ordi-
nary mortals in their answer to our second
question. In fact, almost all philosophers,
seem to be agreed IHaOHere is^aTeal'taBTe :;|
th^^almost--€tlP^ree~*fliat, howevei' much
OUT sense-data — colour, shape, sm^)othness..
etc.!.— mayldepend upori""us, yet their oc--
currence is a sign of something existing
independently of u^, something diilernr

]:ARANGE ANirWALITY 1 2fe

APPEARANCE

perhaps, completely from our sense-data,
and-~yet.jto be regarded as causing those
sense-data whenever we are in a suitable
relation to the feal table.

Now obviously this point in which the
philosophers are agreed — the view that there
is a real table, whatever its nature may be
— is vitally important, and it will be worth
while to consider what reasons there are for
accepting this view before we go on tothe /
f urtfier-questioR- asrt?cHJT'G^Tra:fiire of the real/ /
table. Our next chapter, therefore, will bc»
concerned with the reasons for supposing/
that there is a real table at all. :> \ \ ,

Before we go farther it will be well to
consider for a moment wkat it is that we
have discovered so far. .lit has appeared
that, if we take any common object of the
sort that is supposed to be known by the
senses, what the senses immediately tell us ;
is not the truth about t^e.^bject as it is
apart from us, but only jhg truth about
certain sense-data which, so far as "Vife can
see, degend upon the relations betweenjiis ^
and the object. Thus wh^^t we directly see

f 'mi ^'Mr^^ -' ''

24 THE PROBLEMS OF PHILOSOPHY

I and feel is merely " appearance," which we

^believe to be a sign of some "reality"

behind. But if the reality is not what

appears, have we any means of knowing

whether there is any I'ealrtlT'at^air? And if

sonSave we any means of finding out what
it is like ?

Such questions are bewildering, and it is
difficult to know that even the strangest
hypotheses may not be true. Thus our
familiar table, which has roused but the
slightest thoughts in us hitherto, has become
^ problem full of surprising possibilities,
^he one thing we know about it is that it
is not what it seems. Beyond this modest
result, so far, we have the most complete
liberty of conjecture. Leibniz tells us.. it
is a community of souls ; Berkeley tells us
it is an idea in the mind of God ; sober
science, scarcely less wonderful, tells us it
is a vast collection of electric charges in
violent motion.

Among these surprising possibilities, doubt
suggests that perhaps there is no table at all.
Philosophy, if it cannot answer so many

APPEARANCE AND REALITY 25

questions as we could wish, has at least the
power of ashing questions which increase
the interest of the world, and show the
strangeness and wonder lying just below the
surface even in the commonest things of
daily life.

CHAPTER II

THE EXISTENCE OF MATTER

^ In this chapter we have to ask ourselves
whether, in any sense at all, there is such a
thing as matter. Is there a table which
has a certain intrinsic nature, and continues
to exist when -I am^jxpt Jooking, or is the table
merely a product of my imagination,„^dream-
table in a very prolonged dream ? Tfiis
question is of the greatest importance. For
if wejcannot be sure^of the independent
existence of objects, we cannot be^STi?e-^
the independent existence of other-people's
bodies, and therefore still less of other people's
minds, since we have no grounds for be-
lieving iii their minds except such as are
derived from observing their bodies. Thus
if" we' cannot be sure" of "^ the independent
exlstehce ol o'bjects^'^we^'^ali- be left alone

26

THE EXISTENCE OF MATTER 27

irtf ji, desert — it may be that the whole -,
outer world is^nJothing 6 It K dream, and
that we aTon£exi^. p?his is an uncomfort-
able possibility ; "buf 'although it cannot be
strictly proved to be false, t lere is not the
slightest reason to suppose that it is true.
In this chapter we have to see why this is*
ihe case.

Before we embark upon doubtful matters,
let us try to find some more or less fixed point
from which to start. Although we are
doubting ±he .physical jexi^tence of the taJ5e,
w^^acg,^ not doubting the existence of the*^0
sens£tdaia^hichjriade usthijik-thei^'^ a I
tabl^ ; -JQ^ are miL doubting Ihat^ .„3?x:hije y^'Q'^^
look, a certain colbxir andTsEape^ppear to j

us,^>»4- while we-^3Pe5>s^,au£££^^i^ sensation' of-
hardness is experienGed»-43iy *nsl ATT^This,
which is psychological, we are not calling in
question. In fact, whatever else may be
doufet f ul J sQoia..at least pj.. „ou.F mimediate
experi£jiC£S.^eni absolutely certain.

Descartes (15?fB^BKDXthe founder of
modern philosophy, invented a method which
may still be used with profit — the method of

28 THE PROBLEMS OF PHILOSOPHY

sy^tema^ie^ -doubt. He determined that he
would believe nothing which he did not see
quite clearl^and distinctly to be true. What-
ever he could bring himself to doubt, he would
doubt, until he saw reason for not doubting
it. By applying this method he gradually
became convinced that the only existence of
which he could be quite certain was his own.
He imagined a deceitful demon, who pre-
sented unreal things to his senses in a
perpetual phantasmagoria ; it might be very
improbable that such a demon existed, but
still it was possible, and therefore doubt
concerning things perceived by the senses ^
was possible. ^1

But doubt concerning his own existence
was not^^p.^sible, for if he did not exist, no
d^on could deceive him. If he doubted,
'he-irmsfexist ; if he had any experiences
wliateveJvJie must exist. Thus his own ex-
* ist^rrrce -was—an absolute certainty to him.
" I think, therefore I am," he said {Cogito,
ergo sum) ; and on the basis of this certainty
he set to work to build up again the world
of knowledge which his doubt had laid in

THE EXISTENCE OF MATTER 29

ruins. By inventing the method of doubt,
and by" i^hO'Wlng Ih^lL scri»i«ftti3z:e tfajljijgs^ oxdl'^'^

•.,it[e_jnost certain, Descartes performed a
great service to philosophy, and one which
makes him still useful to all students of
the subject.

But some care is n^^ifed-in, using Des-
cartes' argument. Hi /think, therefore fl
am" says rather moiiQlhani^ strictly cer

^ain. It might segjxu-as though 3££_^were

quite s,urec-of^=1Seingthe"~'saTn«-'persQn to-day ~
as we were yesterday, aetd-this is iiU"^"dt>ubF
true in some sense. But the real Self is
as hard to arrive, at as the real table^ and
de«s not" seem to have that absolute, con-
vincing certaiuty that belongs to particular
experiences. When I look at my table and -
see a certain brown colour, what is quite cer-
tain at once js^ not "/ am. seeing a „bxQ3Kn..
colour," but^railieiv-" cl brown «QlQiUMLg.Jbeing
seen." This of^^^co^rsc-^^^v^lvcs-- something
(or somebody) which (or wha)-S€es the brown
colour ; Jhi^t ^^- dops ript of jtsgljMnvolve that
iitJfe'or less permanent person whom we" tall
" I^i -So^ 3ai^^^ftS~immediat(r certainty goes,^

\

■-^e"

1

I

so THE PROBLEMS OF PHILOSOPHY I

^|it might be that the something whicli'

11 sees the brown colour is quite momentarwi
and not the same as the something whichS *

' has some different experience the next J
moment.

t Thus it is our jQarticialjgyL. JJioughJt^„ and
feelings thatjbave^linaitive certainty. And
this applies to dreams and hallucinations as
well as to normal perceptions : when we
dream or see a ghost, we certainly do have
the sensations we think we have, but for
various reasons it is held that no physical
object corresponds to these sensations. Thus
the certainty of our knowledge of our own
exjperiences does not h^ve. to be^ limited in
any way to allow for exceptional cases. Here,
therefore, we have, for what it is worth, a
solid basis from which to begin our pursuit
of knowledge.

'^f , The problem we have to consider is this :
'Granted that we are certain of our own sense-
^ata, have^we any reason for regarding the.ni
|as signs of the existence cf something else,
» which we can call the physic^ object ? Whei
we have enumerated all the sensations wnici

THE EXISTENCE OF MATTER 31

we should naturally regard as connected with
the table, have we said all there is to say-
about the table, or is there still something
else — something not a sensation, something
which persists when we go out of the room ?
Common sense unhesitatingly answers that
there is. What can be bought and sold and
pushed about and have a cloth laid on it,
and so on, cannot be a mere collection of sense-
data. If the cloth completely hides the f
table, we shall derive no sense-data froni
the table, and therefore, if the table werCj .
merely sense-data, it would have ceased to^
exist, and the cloth would be suspended in
empty air, resting, by a miracle, in the place
where the table formerly was. This seems
plainly absurd ; but whoever wishes to be-
come a philosopher must learn not to be
frightened by absurdities. \

One great reas„Qii..why4tisiettThat we must
secure'^'a^'^i^wiaj^object in additioTx..to the /
sense- data, is that w^j^^nt^fee-'^sa^Tiir-ekiect'
for different people. When ten peopje jare^'
stt-tiftg- TomiT3-''u^-3inner^aS[e,^ir^"^s^^ - pfg-—- —
posterous to mamtam that they""aje*T*0t _

'XV*

S2 THE PROBLEMS OF PHILOSOPHY

'^ — S££iiigJJiajsaifte--tabi^Trl5th; the same knives
and f 6rks^-a»d -sfioDJOS^and glasses. But the
sense-data are private to each separate person ;
what* is immediately present to the sight
of one is not immediately present to the j
sight of another : they all see things from ■
slightly different points of view, and therefore j
see them slightly differently. Thus, i:l^here- [
r^rp to be pnhlir n^^i^^f^l ^hjrrtSj whi^h ^nu bff
in-eeme-sense known to many different people,
there must be something over and abpve the

""jrlyaie^ and particular sense«data_which ap-
pear to various people. What reason, then,
Hiave we for belieTing that there are such
— public Tieutral objects ?
^*-^The IBrst answer that naturally occurs to

^ one is that, although different people may
see the table slightly differently, still they all
see more or less similar things when they
look at the table, and the variations in what
they see follow the l^ws of perspective and
reflection of light, so that it is easy to arrive
at a permanent object underlying all the dif-
ferent people's sense-data. I bought my table
\ from the former occupant of my room ; I

THE EXISTENCE OF MATTER 33

could not buy his sense-data, which died""^
when he went away, but I could and did buy
the confident expectation of more or less
similar sense -data. Thus it is the fact that
different people have similar sense-data, and /'
that one person in a given place at different y
times has similar sense-data, which makes /
us suppose that over and above the sense- x
data there is a permanent public object wliich
underlies or causes the sense-data of various

Jeople and various times.
Now -m-ft^^-laiL^s the above considerations
epend upon supposin^jyiiaLjtJi£re^jare„ o^
people besi<^£ja-JW«pscivi^, " 1^
que^Sn nt issue.. — Q%her "people are repre-'"'^
sented to me by certain sense-data, such as
the sight of them or the sound of their voices,
and if I had no reason to believe that there
were physical objects independtinl uf J^py
sens^jzdatayl^'dhfmM-h^^v^lSaTegigon to believe
th£it other j)eople exist except as part of^my-
dream. Thug, when we are trying to show that
there must be objects independent of our own
sense-data, we cannot appeal to the testimony
of other people, since this testimony itself

34 THE PROBLEMS OF PHILOSOPHY

consists of sense-data, and does not reveal
other people's experiences unless our own
sense-data are signs of things existing inde-
pendently of us. We must therefore, if
possible, find, in our own purely private
experiences, characteristics which show, or
tend to show, that there are in the world

j^ things other than ourselves and our private

* experiences.

t^ •jhrrmc acnGfeiLjnustbe admittedtlia£>-we
can never prove thje existence of ffii^gsnotljer
thaa^iEfttrseUsefi — ajid gwj '''!e^^<'Ti^rif*ps . No
logical absurdity results from the hypothesis
that the world consists of myself and my
thoughts and feelings and sensations, and
that everything else is mere fancy. In
dreams a very complicated world may seem
to be present, and yet on waking we find it
was a delusion ; that is to say, we find that
the sense-data in the dream do not appear to
have corresponded with such physical object i
as we should naturally infer from our sense-
data. (It is true that, when the ph;TsicaI
world is assumed, it is possible to find ph; sical
causes for the sense-data in dreams : a door

THE EXISTENCE OF MATTER 35

banging, for instance, may cause us to dream
of a naval engagement. But although, in
this case, there is a physical cause for the
sense-data, there is not a physical object
corresponding to the seiise-dat.i in the^way in
which an actual n.aval battle wonlc^ corre-
spond.) There is no logical impossibility ^ti
the supposition that the whole of life
di^mIIli3L--^bich we ourscr/es create aii tb(^
objects that come before us* J^But cJb^nugh
this is not logically impossible, there is ii.)
reason whatever to suppose that it is true ;
and it is, in fact, a less simple hypothesis, jti^^
viewed a^ /v, means of accounting for the''v*
facts of our own life, than the common-sense
hypothesis that there really are objects inde-
pendent of us, whose action on us causes our
sensations.

The way in which simplicity comes in from *^
supposing that there really are physical
objects is easily seen. If the cat appears at
one moment in one part of the room, and at
another in another part, it is natural to
suppose thai: it has moved from the one to
the other, passing over a series of intermediate

36 THE PROBLEMS OF PHILOSOPHY

positions. But if it is merely a set of sense-
data, it cannot have ever been in any place
where I did not see it ; thus we shall have
to suppose that it did not exist at all while
I was not looking, but suddenly sprang into
being in a new place. Jf the cat exists
whether I see it or not, we can understand
from our own experience how it gets hungry
between one meal and the next ; but if it
does not exist when I am not seeing it, it
seems odd that appetite should grow during /
non-existence as fast as during existence.
And if the cat consists only of sgnse^-datarilr^

.OMXk- csLTt- be ar-sgfise^^tum- to mr.^ Thus
the behaviour of the sense -data which repre-
sent the cat to me, though it seems quite
natural when regarded as an expression of
hunger, becomes utterly inexplicable when
regarded as mere movements and changes
of patches of colour, which are as incapable
of hunger as a triangle is of playing foot-
ball.

But the difficulty in the case of the cat is
nothing compared to the difficulty in the case

THE EXISTENCE OF MATTER 37

of human beings. JVVhen human beings speak
— that is, v/hen we ^^'^^^^^^^^^'*TiTi nnrnt^s ^ryS>h_^^
^we associate with ideas, and simultaneously
see certain motions of lips and ex^ressions-tjf"
face— ;itisji£e*ydtfficult to suppose that what
we hear is not the expression of a thought,
as we- knQ3£IIE"wQuld.-b^ emitted th^ '

ime sounds. Of course similar things happen
dreams, where we are mistaken as to the
dstence of other people. But dreams are
Lore or less suggested by what we call waking v^,
[e, and are capable of being more or less '^^J
accounted for on scientific principles if we
assume that there really is a physical V
world. Thus every pf inTCtpie of --simplieity J^^^^^^
urges us to acTopt the natural view, that 'X,
there really are objects-~-t>ttec_Jhan our
selves and our sense -^ata^ -which hav?^ri'
existence not dependent^U^o^ our perceiving
them, -'""'

IQf course it is not by argument that we
originally come by our belief in an independent
external world. We find this belief ready
in ourselves as soon as we begin to reflect :
it is what may be called an instinctive belief <^

38 THE PROBLEMS OF PHILOSOPHY

We should never have been led to question
this belief but for the fact that, at any rate
in the case of sight, ife/seems as if the sense-
datum itself were instinctively believed to
be the independent object, whereas argument
shows that the object cannot be identical
with the sense-datum. This ^isco very, how-
ever— which is not at all paradoxical in the
case of taste and smell and sound, and only
slightly so in the case of touch — leaves un-
r diminished our instinctive belief that there
art objects corresponding to our sense-data.
Since this belief does not lead to any diffi-
culties, but on the contrary tends to simplify
and systematise our account of our experi-
ences, there seems no good reason for rejecting
it. We may therefore admit — though with
a sK^^ht doubt derived from dreams — that
the external Avorld does really exist, and is not
wholly dependent for its existence up_QQ^ur
continuing to perceive it.

The argument which has led us to this con-
clusion is doubtless less strong than we could
wish, but it is typical of many philor:ophicaI
argum^ents, and it is therefore worth while to

THE EXISTENCE OF MATTER 39

consider briefly its general character and
validity. AIL Jinp\v:Jedge,_ we find, must be
built up upon our instinctive beliefs, and if
these are rejected, nothing is left. But among
our instinctive beliefs some are much stronger
than others, while many have, by habit and
association, become entangled with other
beliefs, not really instinctive, but falsely
supposed to be part cjf what is believed
instinctively.

Philosophy should show us the hierarchy
of our instinctive beliefs, beginning with
those we hold most strongly, and presenting
each as much isolated and as free from irrele-
vant additions as possible. It should take
care to show that, in the form in which they
are finally set forth, our, in§jtinctive beliefs
do not clash, but form a harmonious system. ^ V
There can never be any reason for rejecting
one instinctive belief except that it clashes
with others ; thus, if they are found to har-
monise, the whole system becomes worthy of
acceptance.

It is of course 'possible. \hsX all or any of our
beliefs may be mistaken, and therefore all

40 THE PROBLEMS OF PHILOSOPHY

ought to be held with at least some slight
element of doubt. But we cannot have
reason to reject a belief except on the
ground of some other belief. Hence, by
organising our instinctive beliefs and their
consequences, by considering which among
them it is most possible, if necessary, to
modify or abandon, we can arrive, on
the basis of accepting as our sole data
what we instinctively believe, at an or-
derly systematic organisation of our know-
ledge, in which, though the possibility of
error remains, its likelihood is diminished
by the interrelation of the parts and by
the critical scrutiny which has preceded
acquiescence.

This function, at least, philosophy can per-
form. INJost philosophers, rightly or wrongly,
believe that philosophy can do much more
than this — that it can give us knowledge,
not otherwise attainable, concerning the
universe as a whole, and concerning the nature
of ultimate reality. Whether this be the
case or not, the more modest function we have
spoken of can certainly be performed by

THE EXISTENCE OF MATTER 41

philosophy, and certainly suffices, for those
who have once begun to doubt the adequacy
of common sense, to justify the arduous and
difficult labours that philosophical problems
involve.

CHAPTER III

THE NATURE OF MATTER

/ In the preceding chapter we agreed,
though without being able to find demonstra-
tive reasons, that it is rational to believe that
our sense-data — for example, those which we
regard as associated with my table — are
really signg of the existence of something"
independent of us and our perceptions. That
is to say, over and above the sensations of
colour, hardness, noise, and so on, which
make up the appearance of the table to
me, I assume that there is something else,
of which these things are appearances.
The colour ceases to exist if I shut my
eyes, the sensation of hardness ceases to
exist if I remove my arm from contact
with the table, the sound ceases to exist if
I cease to rap the -table with my knuckles,

42

THE NATURE OF MATTER 43

But I do not believe that when all these
things cease the table ceases. On the
contrary, I believe that . jt is Jbecause the
table exists continuously that all jQiese
sense-data will reappear when I open ^my
eyes, replace my arm, and begin again
to rap with my knuckles. The question'^
we have to consider in this chapter is:
What is the nature of this real table, ,^/
which persists independently of my per-
ception of it ?

To this question physical science gives an
answer, somewhat incomplete it is true, and in
part still very hypothetical, but yet deserving
of respect so far as it goes. Physical science, ^
more or less unconsciouslv, has drifted into
the viejwjhyat jail natural phenomena ought to
be reduced to motipjis. Light and heat and
sound are all due to wave-motions, which
travel from the body emitting them to the
person who sees light or feels heat or hears
sound. That which has the wave-motion is
either aether or " gross matter," but in either
ca se is what the philosopher would call matter.
The only properties which science assigns to

M THE PROBLEMS OF PHILOSOPHll

at are position in spacCj and the power oi
motion according to the laws of motion.]
Science does not deny that it may have othei
properties ; but if so, such other properties!
are not useful to the man of science, and in|
no way assist him in explaining the pheno-
mena.

It is sometimes said that " light is a form'

^f wave-motion," but this is misleading, for

the light which we immediately see, which
-we know directly by means of our senses,
IS not a form of wave-motion, but some-
thing quite different — something which
we all know if we are not blind, though

-^^e cannot describe it so as to convey our
knowledge to a man who is blind. A wave-
motion, on the contrary, could quite welli
be described to a blind man, since he!
can acquire a knowledge of space by
the sense of touch ; and he can experience
a wave-motion by a sea voyage almost 1
as well as we can. But this, which a J
blind man can understand, is not what we 1
mean by light: we mean by light just that ]
which a blind man can never understand, i

THE NATURE OF MATTER 45

and which we can never describe to
him.

Now this something, which all of us who are
! not blind know, is not, according to science,
really to be found in the outer world : it is
something caused by the action of certain
waves upon the eyes and nerves and brain of
the person who sees the light. When it is
said that light is waves, what is really
meant is that w^es are the physical cause
of our sensations of light. But light itself,
the thing which seeing people experience
and blind people do not, is not supposed by
science to form any part of the world that
is independent of us and our senses. And
very similar remarks would apply to other
kinds of sensations.

It is not only colours and sounds and so
on that are absent from the scientific world
of matter, but also^paceas we get it through
sight or touch. It is essential to science that
its matter should be in a space, but the
space in which it is cannot be exactly the
space we see or feel. To begin with, space
as we see it is not the same as space as we

43 THE PROBLEMS OF PHILOSOPHY

get it by the sense of touch ; it is only by
experience in infancy that we learn how to
touch things we see, or how to get a sight |
of things which we feel touching us. But
the space of science is neutral as be-
tween touch and sight; thus it cannot be i
either the space of touch or the space of
sight. 3

Again, different people see the same object •
as of different shapes, according to their :
point of view. A circular coin, for example, !
though we should always judge it to be i
circular, will look oval unless we are ^
straight in front of it. When we judge that i
it is circular, we are judging that it has a ]
real shape which is not its apparent shape, I
but belongs to it intrinsically apart from ^
its appearance. But this real shape, which ;
is what concerns science, rnust be in a real 1
space, not the same as anybody's apparent j
space. The real space is_public^the apparent ]
space is private to the percipient. In difier- j
ent people's private spaces the same object \
seems to have different shapes ; thus the real -
space, in which it has its real shape, mus!; be ]

THE NATURE OF MATTER 47

different from the private spaces. The space —
of science, therefore, though connected with
the space_s_jKe ^see and feel, is not identical
with them, and the manner of its connection
requires investigation.

We agreed provisionally that physicar
objects cannot be quite like our sense-data,
but may be regarded as causing our sen-
sations. These physical objects are in the
space of science, which we may call " physi-
cal " space. It is important to notice that,
if our sensations are to be caused by phy-
sical objects, there must be a physical space
containing these objects and our sense-
organs and nerves and brain. We get a
sensation of touch from an object when
we are in contact with it ; that is to say,
when some part of our body occupies a place
in physical space quite close to the space
occupied by the object. We see an object
(roughly speaking) when no opaque body
is between the object and our eyes in phy-
sical space. Similarly, we only hear or smell
or taste an object when we are sufficiently
netij to it, or when it touches the tongue.

48 THE PROBLEMS OF PHILOSOPHY

or has some suitable position in physical
space relatively to our body. We cannot
begin to state what different sensations
we shall derive from a given object under
different circumstances unless we regard the
object and our body as both in one physical
space, for it is mainly the relative positions
of the object and our body that determine
what sensations we shall derive from the
object.

Now our sense-data are situated in our
private spaces, either the space of sight or
the space of touch or such vaguer spaces
as other senses may give us. If, as science
and common sense assume, there is one
public all-embracing physical space in which
physical objects are, the relative positions of
physical objects in physical space must more
or less correspond to the relative positions of
sense-data in our private spaces. There is
no difficulty in supposing this to be the case.
If we see on a road one house nearer to us
than another, our other senses will bear
out the view that it is nearer ; for example,
it will be reached sooner if we walk along

THE NATURE OF MATTER 49

the road. Other people will agree that the
house which looks nearer to us is nearer ;
the ordnance map will take the same view ;
and thus everything points to a spatial
relation between the houses corresponding
to the relation between the sense-data which
we see when we look at the houses. Thus we -
may assume that there is a physical space
in which physical objects have spatial re-
lations corresponding to those which the
corresponding sense-data have in our private
spaces. It is this physical space which is
dealt with in geometry and assumed in
physics and astronomy.

Assuming that there is physical space,
and that it does thus correspond to private
spaces, what can we know about it ? We
can know only what is required in order to
secure the correspondence. That is to say,
we can know nothing of what it is like in itself,
but we can know the sort of arrangement
of physical objects which results from their
spatial relations. We can know, for example,
that the earth and moon and sun are in
one straight line during an eclipse, though

50 THE PROBLEMS OF PHILOSOPHY

we cannot know what a physical straight
line is in itself, as we know the look of a
straight line in our visual space. Thus we
come to know much more about the re-
lations of distances in physical space than
about the distances themselves ; we may
know that one distance is greater than
another, or that it is along the same straight
line as the other, but we cannot have that
immediate acquaintance with physical dis-
tances that we have with distances in our
private spaces, or with colours or sounds
or other sense-data. We can know all those
things about physical space which a man
born blind might know through other people
about the space of sight ; but the kind of
things which a man born blind could never
know about the space of sight we also cannot
know about physical space. We can know
the relations required to preserve the cor-
respondence with sense-data, but we cajmot
know the nature of the terms between which
the relations hold.

With regard to time, our feeling of duration
or of the lapse of time is notoriously an

THE NATURE OF MATTER 51

unsafe guide as to the time that has elapsed
by the clock. Times when we are bored or
suffering pain pass slowly, times when we
are agreeably occupied pass quickly, and
times when we are sleeping pass almost as
if they did not exist. Thus, in so far as time
is constituted by duration, there is the same
necessity for distinguishing a public and a
privatje.^ time as there was in the case of
space. But in so far as time consists in
an order of before and after, there is no need
to make such a distinction ; the time-order ^
which events seem to have is, so far as we
can see, the same as the time-order which
they do have. At any rate no reason can
be given for supposing that the two orders are
not the same. The same is u^ii^ly true of r
space : if a regiment of men are marching
along a road, the shape of the regiment will
look different from different points of view,
but the men will appear arranged in the
same order from all points of view. Hence-^
we regard the order as true also in physical
space, whereas the shape is only supposed
to correspond to the physical space so far

52 THE PROBLEMS OF PHILOSOPHY

as is required for the preservation of the
order.

In saying that the time-order which events
seem to have is the same as the time-orier i
which they really have, it is necessary to \
guard against a possible misunderstanding. )
It must not be supposed that the various '\
states of different physical objects have '
the same time-order as the sense-data which ]
constitute the perceptions of those objects. '.
Considered as physical objects, the thunder '
and lightning are simultaneous ; that is ;
to say, the lightning is simultaneous with '
the disturbance of the air in the place \
where the disturbance begins, namely, where i
the lightning is. But the sense-datum ]
which we call hearing the thunder does not \
take place until the disturbance of the air \
has travelled as far as to where we are. \
Similarly, it takes about eight minutes for \
the sun's light to reach us ; thus, when we ;
see the sun we are seeing the sun of eight \
minutes ago. So far as our sense-data \
afford evidence as to the physical sun they j
afford evidence as to the physical sun of !

THE NATURE OF MATTER 53

eight minutes ago ; if the physical sun had
ceased to exist within the last eight minutes,
that would make no difference to the sense-
data which we call " seeing the sun."
This affords a fresh illustration of the neces-
sity of distinguishing between sense-data
and physical objects.

What we have found^as regards space is
much the same as what we find in relation
to the correspondence of the sense-data with
their physical counterparts. If one object
looks blue and another red, we may reason-
ably presume that there is some corresponding
difference between the physical objects ; if
two objects both look blue, we may presume
a corresponding similarity. But we cannot
hope to be acquainted directly with the
quality in the physical object which makes
it look blue or red. Science tells us that
this quality is a certain sort of wave-
motion, and this sounds familiar, because
we think of wave-motions in the space we
see. But the wayej;;motj.cuis ^ must really
be in physical space, with which we have
no direct acquaintance ; thus the real

54 THE PROBLEMS OF PHILOSOPHY

wave - motions have not that familiarity,
which we might have supposed them to
have. And what holds for colours is closely
similar to what holds for other sense-data.
Thus we find that, although the relations
of physical objects have all sorts of know- i
able properties, derived from their corre- \
spondence with the relations of sense-data, ]
the physical objects themselves remain un- i
known in their intrinsic nature, so far at least j
as can be discovered by means of the senses. I
The question remains whether there is any ■
other method of discovering the intrinsic J
nature of physical objects. ■>

" The most natural, though not ultimately "
the most defensible, hypothesis to adopt in the i
first instance, at any rate as regards visual ^
sense-data, would be that, though physical
objects cannot, for the reasons we havejbeeni
considering, be exactly like sense-data, yet ;
they may be more or less like. According to \
this view, physical objects will, for example, '\
really have colours, and we might, by good i
luck, see an object as of the colour it really |
is. The colour which an object seems to '

THE NATURE OF MATTER 55

have at any given moment will in general
be very similar, though not quite the same,
from many different points of view ; we might
[thus suppose the " real " colour to be a sort
of medium colour, intermediate between
the various shades which appear from the
different points of view.

Such a thejQXy is perhaps not capable of
being definitely refuted, but it can be shown
to be groundless. To begin with, it is plain
that the colour we see depends only upon the
nature of the light-waves that strike the eye,
and is therefore modified by the medium
intervening between us and the object, as
well as by the manner in which light is re-
flected from the object in the direction of
the eye. The intervening air alters colours
unless it is perfectly clear, and any strong
reflection will alter them completely. Thus
the colour we see is a result of the ray as it
reaches the eye, and not simply a property
of the object from which the ray comes.
Hence, also, provided certain waves reach
the eye, we shall see a certain colour, whether
the object from which the waves start has

56 THE PROBLEMS OF PHILOSOPHY

any colour or not. Thus it is quite gra-
tuitous to suppose that physical objects
have colours, and therefore there is no
justification for making such a supposition.
Exactly similar arguments will apply to
other sense-data.

- It remains to ask whether there are any
general philosophical arguments enabling us
to say that, if matter is real, it must be of
such and such a nature. As explained above,
very many philosophers, perhaps most, have
held that whatever is real must be in some
sense mental, or at any rate that whatever
we can know anything about must be in some
sense mental. Such philosophers are called
*' idealists." Idealists tell us that what ap-
pears as matter is really something mental ;
namely, either (as Leibniz held) more or less
rudimentary minds, or (as Berkeley contended)
ideas in the minds which, as we should com-
monly say, " perceive " the matter. Thus
idealists deny the existence of matter as
something intrinsically different from mind,
though they do not deny that our sense-data
are signs of something which exists inde-

THE NATURE OF MATTER 57

pendently of oui^jprivate sensations. In the
following chapter we shall consider briefly
the reasons — in my opinion fallacious —
which idealists advance in favour of their
theory.

CHAPTER IV /

IDEALISM I

The word " idealism " is used by different i
philosophers in somewhat different senses. \
We shall understand by it the doctrine-that \
/whatever exists, or.at jany„ratQ jvhatever can
be known to exist, must be in some sense '
mental. This doctrine, which is very widely !
held among philosophers, has several forms,
and is advocated on several different grounds. !
The doctrine is so widely held, and so in- j
teresting in itself, that even the briefest ^
survey of philosophy must give some ac- ]
count of it. ^

Those who are unaccustomed to philo- <
sophical speculation may be inclined to '
dismiss such a doctrine as obviously absurd. |
There is no doubt that common sense regards I
tables and chairs and the sun and moon and 1

58 \

IDEALISM 6d

material objects generally as something radic-
ally different from minds and the contents of
minds, and as having an existence which
might continue if minds ceased. We think
of matter as having existed long before there
were any minds, and it is hard to think of it
as a mere product of mental activity. But
whether true or false, idealism is not to be
dismissed as obviously absurd.

We have seen that, even if physical objects \^
do have an independent existence, they must
differ very widely from sense-data, and can
only have a correspondence with sense-data,
in the same sort of way in which a catalogue
has a correspondence with the things cata-
logued. Hence common sense leaves us
completely in the dark as to the true intrinsic
nature of physical objects, and if there were
good reason to regard them as mental, we
could not legitimately reject this opinion
merely because it strikes us as strange. The
truth about physical objects must be strange.
It may be unattainable, but if any philosopher
believes that he has attained it, the fact that
what he offers as the truth is strange ought

60 THE PROBLEMS OF PHILOSOPHY

not to be made a ground of objection to his ^^1
opinion. »H

^ The grounds on which ideahsm is advocated Ij

are generally grounds derived from the theory I

of knowledge, that is to say, from a discussion '-
of the conditions which things must satisfy

in order that we may be able to know them. \

The first serious att^JPapLL-to establish idealism 1

on such grounds was that of Bishop Berkeley. !

He proved first, by arguments which were *

largely valid, that our sense-data cannot be \
supposed to have an existence independent

of us, but must be, in part at least, " in "_ \

the mind, in the sense that their existence \

would not continue if there were no seeing I

or hearing or touching or smelling or tasting. \
So far, his contention was almost certainly

valid, even if some of his arguments were not \

so. But he went on to argue that sense-data \

were the only things of whose existence our 1

perceptions could assure us, and that to be \

known is to be " in " a mind, and therefore '\

to be mental. Hence he concluded that ]

nothing can ever be known except what is in 1

some mind, and that whatever is known ]

IDEALISM 61

without being in my mind must be in some
other mind.

In order to understand his argument, it is
necessary to understand his use of the word
" idea." He gives the name " idea " to any-
thing which is immediately known, as, for
example, sense-data are known. Thus a par-
ticular colour which we see is an idea ; so is
a voice which we hear, and so on. But the
term is not wholly confined to sense-data.
There will also be things remembered or
imagined, for with such things also we have
immediate acquaintance at the moment of
remembering or imagining. All such im-
mediate data he calls *' ideas."

He then proceeds to consider common
objects, such as a tree, for instance. He shows
that all we know immediately when we " per-
ceive " the tree consists of ideas in his sense
of the word, and he argues that there is not
the slightest ground for supposing that there
is anything real about the tree except what is
perceived. Its being, he says, consists in
being perceived : in the Latin of the school-
men its " esse " is " percipi." He fully admits

62 THE PROBLEMS OF PHILOSOPHY

that the tree must continue to exist even when
we shut our eyes or when no human being is
near it. But this continued existence, he
says, is due to the fact that God continues to
perceive it ; the " real " tree, which corre-
sponds to what we called the physical object,
consists of ideas in the mind of God, ideas
more or less like those we have when we see
the tree, but differing in the fact that they are
permanent in God's mind so long as the tree
continues to exist. All our perceptions,
according to him, consist in a partial parti-
cipation in God's perceptions, and it is
because of this participation that different
people see more or less the same tree. Thus
apart from minds and their ideas there is
nothing in the world, nor is it possible that
anything else should ever be known, since
whatever is known is necessarily an idea.

There are in this argument a good many
fallacies which have been important in the
history of philosophy, and which it will be
as w^ell to bring to light. In the.gr^t place,
there is a confusion engender^.d by... tJxe.. use
of the word " idea.'! We think of an idea

IDEALISM 63

as essentially something in somebody's mind,
and thus when we are told that a tree consists
entirely of ideas, it is natural to suppose that,
if so, the tree must be entirely in minds. But
the notion of being " in " the mind is am-
biguous. We speak of bearing a person in
mind, not meaning that the person is in our
minds, but that a thought of him is in our
minds. When a man says that some business
he had to arrange went clean out of his mind,
he does not mean to imply that the business
itself was ever in his mind, but only that a
thought of the business was formerly in his
mind, but afterwards ceased to be in his
mind. And so when Berkele.y says that the
tree niust be ia^oiULXoijids.if jve can know it,
all that he really has a right to say is that a
thought of the tree must be in our minds. To
argue that the tree itself must be in our minds
is like arguing that a person whom we bear
in mind is himself in our minds. This con-,
fusion may seem too gross to have been really
committed by any competent philosopher,
but various attendant circumstances rendered
it possible. In order to see how it was^

64 THE PROBLEMS OF PHILOSOPHY

possible, we must go more deeply into the
question as to the nature of ideas.

Before taking up the general question of
the nature of ideas, we must disentangle two*^
entirely separate questions which arise con-
cerning sense-data and physical objects. We
saw that, for various reasons of detail,
Berkeley was right in treating the sense-data
which constitute our perception of the tree
as more or less subjective, in the sense that
they depend upon us as much as upon the
tree, and would not exist if the tree were not
being perceived. But this is an entirely
different point from the one by which
Berkeley_seeks to prove that whatever can be
immediately known must be in a mind. For
this purpose arguments of detail as to the de-
pendence of sense-data upon us are useless.
It is necessary to prove, generally, that by
being known, things are shown to be mental.
This is what Berkeley believes himself to
have done. It is this question, and not our
previous question as to the difference between
sense-data and the physical object, that must
now concern us.

IDEALISM 65

Taking the word *' idea " in Berkeley's
sense, there are two quite distinct thiij^gs to *^
be considered whenever an idea is before the
mind. There is on the one hand the thing ;
of which we are aware — say the colour of
my tahje — and on the other hand the actual :
awareness itself, the mental act of appre-
hending the thing. The mental act is un-
doubtedly mental, but is there any reason
to suppose that the thing apprehended is
in any sense mental ? Our previous argu-
ments concerning the colour did not prove
it to be mental ; they only proved that its
existence depends upon the relation of our
sense organs to the physical object — in our
case, the table. That is to say, they proved
that a certain colour will exist, in a certain
light, if a normal eye is placed at a certain
point relatively to the table. They did^jiQJt
prove that the colour is in the mincLof the
percipient. ^

Berkeley's view, that obviously the colour ^^
must be in the mind, seems to depend for its
plausibility upon confusing the thing appre-
hended with the act of apprehension. Either
o

66 THE PROBLEMS OF PHILOSOPHY

of these might be called an " idea " ; probably
either would have been called an idea by
Berkeley. The act is undoubtedly in the
mind ; hence, when we are thinking of the .
act, we readily assent to the view that ideas j
must be in the mind. Then, forgetting that I
this was only true when ideas were taken !
as acts of apprehension, we transfer the pro- j
position that " ideas are in the mind " to ;
ideas in the other sense, i.e. to the things \
apprehended by our acts of apprehension. ]
Thus, by an unconscious equivocation^^we i
arrive at the conclusion that whatever we )
can apprehend must be in our minds. This I
seems to be the true analysis of Berkeley's j
argument, and the ultimate fallacy upon I
which it rests. I

This question of the distinction between |
act and object in our apprehending of things *]
is vitally important, sinc^ our whole power ]
of acquiring knowledge is bound up with it. j
The faculty of being acquainted with things j
other than itself is the ihairi^'Characteristic \
of a mind. Acquaintance with objects essen- j
tially consists in a relation between t^ie mind ^

IDEALISM 67 i

I

and something other than the mind ; it is i^ !
this that constitutes the mind's power of

knowing things. If we say that the things ^

known must be in the mind, we are either \

unduly limiting the mind's power of knowing, o^J

or we are uttering a mere tautology. We 4.,

are uttering a mere tautology if we mean by .

" in the mind " the same as by " before the ^ "^-^

mind," i.e. if we mean merely being appre- ^^T

hended by the mind, But if we mean this, ^-^i

we shall have to admit that what, in this ^'.M \

sense, is in the mind, may nevertheless be not ^
mental. Thus when we realise the nature of

knowledge, Berkeley's argument is seen to \

be wrong in silbstance as well as in form, and \
his grounds for supposing that " ideas " — i.e.

the objects apprehended — must be mental, ]
are found to have no validity whatever.

Hence his grounds in favour of idealism may ^ \

be dismissed. It remains to see whether I

there are any other grounds. \

It is often said, as though it were a self- \
evident truism, that we cannot know that i

anything exists which we do not know. It \

is inferred that whatever can in any way be \

68 THE PROBLEMS OF PHILOSOPHY

relevant to our experience must be at least
capable of being known by us ; whence it

• follows that if matter were essentially^some-
thing with which we could not become ac-
quainted, matter would be something which
we could not know to exist, and which could
have for us no importance whatever. It is
generally also implied, for reasons which
remain obscure, that what can have no im-
portance for us cannot be real, and that
therefore matter, if it is not composed of
minds or of mental ideas, is impossible and a
mere chimsera.

To go into this argument fully at our
present stage would be impossible, since it
raises points requiring a considerable pre-
liminary discussion ; but certain reasons for
rejecting the argument may be noticed at

*^ once. To begin at the end : there Jsjao
reason why what cannot have any practical
importance for us should not be real. It is
true that, if theoretical importance is included,
everything real is of some importance to us,
since, as persons desirous of knowing the
truth about the universe, we have some

IDEALISM 69

Interest in everything that the universe
contains. But if this sort of interest is
included, it is not the case that matter has no
importance for us, provided it exists, even
if we cannot know that it exists. We can,
obviously, suspect that it may exist, and
wonder whether it does ; hence it is con-
nected with our desire for knowledge, and
has the importance of either satisfying or
thwarting this desire.

Again, it is by no mean& a truism,^ and
is in fact false, that we cannot know
that anything exists which we do not know.
The word " know " is here used in two differ-
ent senses. (1) In its first use it is applicable
to the sort of knowledge which is opposed to
error^«the sense in which what we know is
true, the sense which applies to our beliefs
and convictions, i.e. to what are called judg-
ments. In this .sense of the word^jwe know
that something is the case. This sort of know-
ledge may be described as knowledge of truths,
(2) In the second use of the word " know "
above, the word applies to our knowledge of
things, which we may call acquaintance. This

70 THE PROBLEMS OF PHILOSOPHY

is the sense in which we know sense-data.
(The distinction involved is roughly that
between savoir and connaitre in French, or
between wissen and kennen in German.)

Thus the statement which seemed like a
truism becomes, when re-stated, the following :
" We can never truly judge that something
with which we are not acquainted exists."
This is by no means a truism, but on the
contrary a palpable falsehood. I have not
the honour to be acquainted with the Emperor
of China, but I truly judge that he exists. It
may be said, of course, that I judge this be-
cause of other people's acquaintance with him.
This, however, would be an irrelevant retort,
since, if the principle were true, I could not
know that any one else is acquainted with
him. But further : theiig^is iio reason why I
should not know of the existence of something
with which nobody is acquainted. Thi^ point
is important, and demands elucidation.

If I am acquainted with a thing which
exists, my acquaintance gives me the know-
ledge that it exists. But it is not true that,
conversely, whenever I can know that a

IDEALISM 71

thing of a certain sort exists, I or some one
else must be acquainted with the thing.
What happens, in cases where I have true>^
judgment without acquaintance, is that the
thing is knowa-taiRe^by descri'ption, and that,
in virtue of some general principle, the
existence of a thing answering to this de-
scription can be inferred from the existence
of something with which I am acquainted.
In order to understand this point fully, it
will be wxll first to deal with the difference
between knowledge by acquaintance and
knowledge by description, and then to con-
sider what knowledge of general principles,
if any, has the same kind of certainty as our
knowledge of the existence of our own ex-
periences. These subjects will be dealt with
in the following chapters.

CHAPTER V

KNOWLEDGE BY ACQUAINTANCE AND KNOW-
LEDGE BY DESCRIPTION

In the preceding chapter we saw that
there are two sorts of knowledge : knowledge
of things, and knowledge of truths. In this
chapter we shall be concerned exclusively
t^with knowledge of things, of which in turn we
shall have to distinguish two kinds. Know-
ledge of things, when it is of the kind we
call knowledge by acquaintance, is essentially
simpler than any knowledge of truths, and
logically independent of knowledge of truths,
though it would be rash to assume that human
beings ever, in iact, have acquaintance with
things without at the same time knowing
some truth about them. Knowledge of things
by description, on the contrary, always in-
volves, as we shall find in the course of the
72

ACQUAINTANCE AND DESCRIPTION 73

preseilt chapter, some knowledge of truths as
its source and ground. But first of all we
must make clear what we mean by " acquaint-
ance " and what we mean by " description."

We shall say that we have acquaintance t^
with anything of which we are directly aware,
without the intermediary of any process of
inference or any knowledge of truths. Thus
in the presence of my table I am acquainted
with the sense -data that make up the appear-
ance of my table— its colour, shape, hardness,
smoothness, etc. ; all these are things of
which I am immediately conscious when I am
seeing and touching my table. The particular
shade of colour that I am seeing may have
many things said about it — I may say that it
is brown, that it is rather dark, and so on.
But such statements, though they make me
know truths about the colour, do not make me
know the colour itself any better than I did X
before : so far as concerns knowledge of the
colour itself, as opposed to knowledge of
truths about it, I know the colour perfectly
and completely when I see it, and no further
knowledge of it itself is even theoretically

74 THE PROBLEMS OF PHILOSOPHY

possible. Thus the sense-data which make
up the appearance of my table are things
with which I have acquaintance, things im-
mediately known to me just as they are.

My knowledge of the table as a physical
object, on the contrary, is not direct know-
ledge. Such as it is, it is obtained through
acquaintance with the sense-data that make
up the appearance of the table. We have
seen that it is possible, without absurdity, to
doubt whether there is a table at all, whereas
it is not possible to doubt the sense-data. My
knowledgejof^he table is of the kind which^e
shall call " knowledge by description." The
table is " the physical object which causes
such-and-such sense-data." This describes
the table by means of the sense-data. In
order to know anything at all about the
table, we must know truths connecting it
with things with which we have acquaint-
ance : we must know that " such-and-such
sense-data are caused by a physical object."
There is no state of mind in which we are
directly aware of the table ; all our know-
ledge of the table is really knowledge of

ACQUAINTANCE AND DESCRIPTION 75

truths, and the actual thing which is the
table is not, strictly speaking, known to us
at all. We know a description, and we know
that there is just one object to which this
description applies, though the object itself
is not directly known to us. In such a case,
we say that our knowledge of the object is
knowledge by description.

All our knowledge, both knowledge of/
things and knowledge of truths, rests upon
acquaintance as its foundation. It is there-
fore important to consider what kinds of
things there are with which we have acquaint-
ance.

Sense-data, as we have already seen, are
among the things with which we are ac-
quainted ; in fact, they supply the most
obvious and striking example of knowledge
by acquaintance. But if they were the sole
example, our knowledge would be very much
more restricted than it is. We should only
know what is now present to our senses : we
could not know anything about the past — not
even that there was a past — nor could we
know any truths about our sense-data, for all

76 THE PROBLEMS OF PHILOSOPHY

knowledge of truths, as we shall show, de-
mands acquaintance with things which are of
an essentially different character from sense-
data, the things which are sometimes called
, , " abstract ideas," but which we shall call
\ " universals." We have therefore to con-
sider acquaintance with other things besides
sense-data if we are to obtain any tolerably
adequate analysis of our knowledge.
^ The first extension beyond sense-data to
be considered is acquaintance hy memory.
It is obvious that we often remember what
we have seen or heard or had otherwise
present to our senses, and that in such cases
we are still immediately aware of what we
remember, in spite of the fact that it appears
as past and not as present. This immediate
knowledge by memory is the source of all
our knowledge concerning the past : without
it, there could be no knowledge of the past by
inference, since we should never know that
there was anything past to be inferred.
3 The next extension to be considered is
acquaintance by introspection. We_are not
only aware of things, but we are often aware

ACQUAINTANCE AND DESCRIPTION 77

of being aware of them. When I see the sun,
I am often aware of my seeing the sun ; thus
" my seeing the sun ^' is an object with which
I have acquaintance. When I desire food, I
may be aware of my desire for food ; thus
*' my desiring food " is an object with which
I am acquainted. Similarly we may be
aware of our feeling pleasure or pain, and
generally of the events which happen in our
minds. This kind of acquaintance, which
may be called self-consciousness, is the source
of all our knowledge of mental things. It is
obvious that it is only what goes on in our
own minds that can be thus known imme-
diately. What goes on in the minds of others
is known to us through our perception of their
bodies, that is, through the sense-data in us
which are associated with their bodies. But
for our acquaintance with the contents of our
own minds, we should be unable to imagine
the minds of others, and therefore we could
never arrive at the knowledge that they have
minds. It seems natural to suppose that
self-consciousness is one of the things that
distinguish men from animals: animals, we

78 THE PROBLEMS OF PHILOSOPHY

may suppose, though they have acquaintance^
with sense-data, never become aware of thisa
acquaintance, and thus never know of their
own existence. I do not mean that they
doubt whether they exist, but that they have
never become conscious of the fact that they
have sensations and feeHngs, nor therefore of
the fact that they, the subjects of their
sensations and feeHngs, exist.

We have spoken of acquaintance with the

contents of our minds as 5eZ/-consciousness,

jbut it is not, of course, consciousness of our

[self : it is consciousness of particular

thoughts and feeHngs. The question whether

we are also acquainted with om bare selves,

as opposed to particular thoughts and feeHngs,

is a very difficult one, upon which it would

be rash to speak positively. When we try to

look into ourselves we always seem to come

upon some particular thought or feeling, and

not upon the " I " which has the thought or

j feeling. Nevertheless there are some reasons

/ for thinking that we are acquainted with the

) " I," though the acquaintance is har<i to

disentangle from other things. To make clear

ACQUAINTANCE AND DESCRIPTION 79

what sort of reason there is, let us consider for
a moment what our acquaintance with par-
ticular thoughts really involves.

When I am acquainted with " my seeing
the sun," it seems plain that I am acquainted
with two different things in relation to each
other. On the one hand there is the sense-
datum which represents the sun to me, on the
other hand there is that which sees this
sense-datum. All acquaintance, such as my
acquaintance with the sense-datum which
represents the sun, seems obviously a relation
between the person acquainted and the object
with which the person is acquainted. When
a case of acquaintance is one with which I
can be acquainted (as I am acquainted with
my acquaintance with the sense-datum re-
presenting the sun), it is plain that the person
acquainted is myself. Thus, when I am
acquainted with my seeing the sun, the whole
fact with which I am acquainted is " Self-
acquainted-with-sense-datum. "

Further, we know the truth " I am ac-
quainted with this sense-datum." It is hard
to see how we could know this truth, or

80 THE PROBLEMS OF PHILOSOPHY

even understand what is meant by it, unless a
we were acquainted with something which we I
call "I." It does not seem necessary to
suppose that we are acquainted with a more
or less permanent person, the same to-day as
yesterday, but it does seem as though we
must be acquainted with that thing, whatever
its nature, which sees the sun and has ac-
quaintance with sense -data. Thus, in some
sense it would seem we must be acquainted
with our Selves as opposed to our particular
experiences. But the question is difficult,
and complicated arguments can be adduced
on either side. Hence, although acquaintance
with ourselves seems probably to occur, it is
not wise to assert that it undoubtedly does
occur.
^ We may therefore sum up as follov/s what
has been said concerning acquaintance with
things that exist. We have acquaintance in
sensation with the data of the outer senses,
and in introspection with the data of what
may be called the inner sense — thoughts,
feelings, desires, etc. ; we have acquaintance
in memory with things which have been data

ACQUAINTANCE AND DESCRIPTION 81

either of the outer senses or of the inner sense.
Further, it is probable, though not certain, that
we have acquaiiLtan£fi^ith~Self , as that which
is aware of things or has desires towards things.

In addition to our acquaintance with parti- ^
cular existing things, we also have acquaint-
ance with what we shall call universjals, that
is to say, general ideas, such as whiteness,
diversity, brotherhood, and so on. Every com-
plete sentence must contain at least one word
which stands for a universal, since all verbs
have a meaning which is universal. We shall
return to universals later on, in Chapter IX ;
for the present, it is only necessary to guard
against the supposition that whatever we can
be acquainted with must be something parti-
cular and existent. Awareness of universals
is called conceiving, and a universal of which
we are aware is called a concept

It will be seen that among the objects with
which we are acquainted are not included
physical objects (as opposed to sense-data),
nor other people's minds. These things are
known to us by what I call " knowledge by
description," which we must now consider.

82 THE PROBLEMS OF PHILOSOPHY

By a " description " I mean any phrase of
the form " a so-and-so " or "the so-and-so."
A phrase of the form " a so-and-so " I shall

" call an " anaMgumisJijdescwption ; a phrase
of the form " the so-and-so " (in the singular)

- I shall call a " dgfinite^jdescri^tion. Thus
" a man " is an ambiguous description, and
" the man with the iron mask " is a definite
description. There are various problems con-
nected with ambiguous descriptions, but I
pass them by, since they do not directly con-
cern the matter we are discussing, which is the
nature of our knowledge concerning objects
in cases where we know that there is an object
answering to a definite description, though
we are not acquainted with any such object.

I This is a matter which is concerned exclusively
with definite descriptions. I shall therefore, in
the sequel, speak simply of " descriptions "
when I mean " definite descriptions." Xlni^.
•a^-ikscription jnll_n^^^ -oi- the

fQjrn^" the so-and-so "in the singular..^
1^ We shall say that an object is " known by
description" when we knpw_. that it is " ^/ie
so-and::§Q^.iig(.„when we know that Miere is

ACQUAINTANCE AND DESCRIPTION 85

oncLjQfcject, and joo more, having a certain
property ; ^nd it will generally be implied
that we do not have knowledge of the same
object bj acquaintance. We know that the
man with the iron mask existed, and many
propositions are known about him ; but we do
not know who he was. We know that the
candidate who gets the most votes will be
elected, and in this case we are very likely also
acquainted (in the only sense in which one
can be acquainted with some one else) with
the man who is, in fact, the candidate who will
get most votes ; but we do not know which of
the candidates he is, i.e. we do not know any
proposition of the form " A is the candidate
who will get most votes " where A is one of
the candidates by name. We shall say that
we have " merely descriptive knowledge '* of
the so-and-so when, although we know that
the so-and-so exists, and although we may
possibly be acquainted with the object which
is, in fact, the so-and-so, yet we do not know
any proposition " « is the so-and-so," where
a is something with which we are acquainted.
When we say " the so-and-so exists," we

84 THE PROBLEMS OF PHILOSOPHY

mean that there is just one object which is the
so-and-so. The proposition " a is the so-and-
so " means that a has the property so-and-so,
and nothing else has. *' Mr. A. is the Unionist
candidate for this constituency " means
" Mr. A. is a Unionist candidate for this
constituency, and no one else is." " The
Unionist candidate for this constituency
exists" means "some one is a Unionist candi-
date for this constituency, and no one else is."
i/ Thus, when we are acquainted with an object
^yhich is the so-and-so, we know that jhe
so-and-so exists ; but we may know that the
so-and-so exists when we are not acquainted
with any object which we know to be the so-
and-so, and even when we are not acquainted
with any object which, in fact, is the so-and-so.
*/ Gemmoft. words, even pxoper names, are
ilSjiallj^ really desm^jans. That is to say,
the thought in the mind of a person using a
proper name correctly can generally only be
expressed explicitly if we replace the proper
name by a description. Moreover, the de-
scription required to express the thought will
vary for different people, or for the same

ACQUAINTANCE AND DESCRIPTION 85

person at different times. The only thing
constant (so long as the name is rightly used)
is the object to which the name applies. But
so long as this remains constant, the particular
description involved usually makes no differ-
ence to the truth or falsehood of the proposi-
tion in which the name appears.

Let us take some illustrations. Suppose
some statement made about Bismarck. As-
suming that there is such a thing as direct
acquaintance with oneself, Bismarck himself
might have used his name directly to desig-
nate the particular person with whom he was
acquainted. In this case, if he made a
judgment about himself, he himself might be
a constituent of the judgment. Here the
proper name has the direct use which it
always wishes to have, as simply standing for
a certain object, and not for a description
of the object. But if a person who knew
Bismarck made a judgment about him, the
case is different. What this person was ac-
quainted with were certain sense-data which
he connected (rightly, we will suppose) with
Bismarck's body. His body, as a physical

86 THE PROBLEMS OF PHILOSOPHY

object, and still more his mind, were only
known as the body and the mind connected
with these sense-data. That is, they were
known by description. It is, of course, very
.much a matter of chance which character-
istics of a man's appearance will come into a
friend's mind when he thinks of him ; thus
the description actually in the friend's mind
_is accidental. The essential point is that he
knows that the various descriptions all apply
to the same entity, in spite of not being ac-
quainted with the entity in question.

When we, who did not know Bismarck,
make a judgment about him, the description
in our minds will probably be some more or
less vague mass of historical knowledge — far
more, in most cases, than is required to iden-
tify him. But, for the sake of illustration, let
us assume that we think of him as " the first
Chancellor of the German Empire." Here
all the words are abstract except " German.''
The word " German" will, again, have differ-
ent meanings for different people. To some it
will recall travels in Germany, to some the
look of Germany on the map, and so on. But

ACQUAINTANCE AND DESCRIPTION 87

if we are to obtain a description which we
know to be applicable, we shall be compelled,
at some point, to bring in a reference to a
particular with which we are acquainted.
Such reference is involved in any mention of
past, present, and future (as opposed to
definite dates), or of here and there, or of what
others have told us. Thus it would seem that,
in some way or other, a description known to'
be applicable to a particular must involve
some reference to a particular with which we
are acquainted, if our knowledge about the
thing described is not to be merely what
follows logically from the description.

For example, " the most long-lived of men "
is a description which must apply to some
man, but we can make no judgments con-
cerning this man which involve knowledge
about him beyond what the description gives.
If, however, we say, " The first Chancellor of
the German Empire was an astute diplo-
matist," we can only be assured of the truth
of our judgment in virtue of something with
which we are acquainted — usually a testimony
heard or read. Apart from the information

88 THE PROBLEMS OF PHILOSOPHY

we convey to others, apart from the fact about
the actual Bismarck, which gives importance
to our judgment, the thought we really have
contains the one or more particulars involved,
and otherwise consists wholly of concepts.

All names of places — London, England,
Europe, the Earth, the Solar System — simi-
larly involve, when used, descriptions which
start from some one or more particulars with
which we are acquainted. I suspect that even
the Universe, as considered by metaphj^sics,
involves such a connection with particulars.
In logic, on the contrary, where we are
concerned not merely with what does exist,
but with whatever might or could exist or
be, no reference to actual particulars is
involved.

It would seem that, when we make a
statement about something only known by
description, we often intend to make our
statement, not in the form involving the
description, but about the actual thing de-
scribed. That is to say, when we say any-
thing about Bismarck, we should like, if we
could, to make the judgment which Bismarck

I

ACQUAINTANCE AND DESCRIPTION 89

alone can make, namely, the judgment of
which he himself is a constituent. In this
we are necessarily defeated, since the actual
Bismarck is unknown to us. But we know
that there is an object B, called Bismarck,
and that B was an astute diplomatist. We
can thus describe the proposition we should
like to affirm, namely, " B was an astute diplo-
matist," where B is the object which was
Bismarck. If we are describing Bismarck as
" the first Chancellor of the German Empire,"
the proposition we should like to affirm may
be described as " the proposition asserting,
concerning the actual object which was the
first Chancellor of the German Empire, that
this object was an astute diplomatist."
What enables us to communicate in spite of '^
the varying descriptions we employ is that
we know there is a true proposition concerning
the actual Bismarck, and that however we
may vary the description (so long as the
description is correct) the proposition de-
scribed is still the same. This proposition,^
which is described and is known to be true,
is what interests us ; but we are not acquainted

90 THE PROBLEMS OF PHILOSOPHY

with the proposition itself, and do not know
it, though we know it is true.

It will be seen that there are various stages
in the removal from acquaintance with
particulars : there is Bismarck to people who
knew him, Bismarck to those who only know
of him through history, the man with the
iron mask, the longest -lived of men. These
are progressively further removed from ac-
quaintance with particulars ; the first comes
as near to acquaintance as is possible in
regard to another person ; in the second, we
shall still be said to know "who Bismarck
was " ; in the third, we do not know who
was the man with the iron mask, though we
can know many propositions about him which
are not logically deducible from the fact that
he wore an iron mask ; in the fourth, finally,
we know nothing beyond what is logically
deducible from the definition of the man.
There is a similar hierarchy in the region of
universals. Many universals, like many par-
ticulars, are only known to us by description.
But here, as in the case of particulars, know-
ledge concerning what is known by descrip-

ACQUAINTANCE AND DESCRIPTION 91

tion is ultimately reducible to knowledge
concerning what is known by acquaintance.

The fundamental principle in the analysis *^
of propositions containing descriptions is this :
'Every proposition which we can understand
must be composed wholly of constituents with
which we are acquainted.

We shall not at this stage attempt to
answer all the objections which may be urged
against this fundamental principle. For the
present, we shall merely point out that, in
some way or other, it must be possible to
meet these objections, for it is scarcely
conceivable that we can make a judgment
or entertain a supposition without knowing
what it is that we are judging or supposing
about. We must attach some meaning to
the words we use, if we are to speak signi-
ficantly and not utter mere noise ; and the
meaning wft.att^ach Jp_oj3JL.\YOXdfi, jmustJbe
SQtgething with^jsJugh-JSZ^ .M£ ..a©q«€kinted.
Thus when, for example, we make a state-
ment about Julius Caesar, it is plain that
Julius Csesar himself is not before our minds,
since we are not acquainted with him. We

92 THE PROBLEMS OF PHILOSOPHY I

have in mind ^om^^jAescrij^tion of Julius
Caesar : " the man who was assassinated on
the Ides of March," " the founder of the
Roman Empire,'* or, perhaps, merely " the
man whose name was Julius Ccesar." (In
this last description, Julius Ccesar is a noise or
shape with which we are acquainted.) Thu^ur
statement does not mean quite what it seems
to mean, but pieans something involving,
instead of Julius Caesar, some description of
him which is composed wholly of particulars
and universals with which we are acquainted.
The chief- impeftafiee -of knowledge by
description is- that- it -^lables- us to pass
bexQBdjyhgJimJis.jof-0^
In spite of the fact that we can only know
truths which are wholly composed of terms
which we have experienced in acquaintance,
we can yet have knowledge by description
of things which we have never experienced.
In view of the very narrow range of our
immediate experience, this result is vital,
and until it is understood, much of our know-
ledge must remain mysterious and therefore
doubtful.

I

i

CHAPTER VI

ON INDUCTION

In almost all our previous discussions we
have been concerned in the attempt to get
clear as to our data in the way of knowledge
of existence. What things are there in the
universe whose existence is known to us owing
to our being acquainted with them ? So far,
our answer has been that we are acquainted
with our sense-data, and, probably, with our-
selves. These we know to exist. And past
sense-data which are remembered are known
to have existed in the past. This know-
ledge supplies our data.

But if we are to be able to draw inferences ^
from these data — if we are to know of the
existence of matter, of other people, of the
past before our individual memory begins,
or of the future, we must know general prin-
03

94 THE PROBLEMS OF PHILOSOPHY

ciples of some kind by means of which such
inferences can be drawn. It must be known
»to us that the existence of some one sort of
thing, A, is a^ sign of the existence of some
other sort of thing, B, either at the same time
as A or at some earher or later time, as, for
example, thunder is a sign of the earlier
existence of lightning. If this were not known ♦
to us, we could never extend our knowledge
beyond the sphere of our private experience ;
and this sphere, as we have seen, is exceed-
ingly limited. The question we have now to
consider is whether such an extension is
possible, and if so, how it is effected.

Let us take as an illustration a matter about
which none of us, in fact, feel the slightest
doubt. We are all convinced that the sun
will rise to-morrow. Why ? Is this belief a
mere blind outcome of past experience, or
can it be justified as a reasonable belief ? It
is not easy to find a test by which to judge
whether a belief of this kind is reasonable or
not, but we can at least ascertain what sort
of general beliefs would suffice, if true, to
justify the judgment that the sun will rise

ON INDUCTION 95

to-morrow, and the many other similar judg-
ments upon which our actions are based.

It is obvious that if we are asked why we
believe that the sun will rise to-morrow, we
shall naturally answer, " Because it always
has risen every day." We have a firm belief
that it will rise in the future, because it has
risen in the past. If we are challenged as to *
why we believe that it will continue to rise
as heretofore, we may appeal to the laws of
motion : the earth, we shall say, is a freely
rotating body, and such bodies do not cease
to rotate unless something interferes from
outside, and there is nothing outside to
interfere with the earth between now and
to-morrow. Of course it might be doubted
whether we are quite certain that there is
nothing outside to interfere, but this is not
the interesting doubt. The interesting
doubt is as to whether the laws of motion
will remain in operation until to-morrow. If
this doubt is raised, we find ourselves in the
same position as when the doubt about the
sunrise was first raised.

The only lesLSon for believing that the laws

96 THE PROBLEMS OF PHILOSOPHY

of motion will remain in operation is that
they have operated hitherto, so far as our
knowledge of the past enables us to judge.
It is true that we have a greater body of
evidence from the past in favour of the laws
of motion than we have in favour of the sun-
rise, because the sunrise is merely a particular
case of fulfilment of the laws of motion, and
there are countless other particular cases.
t^But the real question is : Do any number
of cases of a law being fulfilled in the past
afford evidence that it will be fulfilled in the
future ? If not, it becomes plain that we
have no ground whatever for expecting the
sun to rise to-morrow, or for expecting the
bread we shall eat at our next meal not to
poison us, or for any of the other scarcely
conscious expectations that control our daily
lives. It is to be observed that all such
expectations are only probable ; thus we have
not to seek for a proof that they must be ful-
filled, but only for some reason in favour of
the view that they are likely to be fulfilled.

Now in dealing with this question we must,
to begin with, make an important distinction.

I

ON INDUCTION 97

without which we should soon become in-
volved in hopeless confusions. Experience
has shown us that, hitherto, the frequent
repetition of some uniform succession or
coexistence has been a cause of our expecting
the same succession or coexistence on the
next occasion. Food that has a certain
appearance generally has a certain taste, and
it is a severe shock to our expectations when
the familiar appearance is found to be asso-
ciated with an unusual taste. Things which
^e see become associated, by habit, with
certain tactile sensations which we expect
if we touch them ; one of the horrors of a
ghost (in many ghost-stories) is that it fails
to give us any sensations of touch. Unedu-
cated people who go abroad for the first time
are so surprised as to be incredulous when
they find their native language not under-
stood.

And this kind of association is not confined
to men ; in animals also it is very strong.
A horse which has been often driven along a
certain road resists the attempt to drive him
in a different direction. T)omestic animals

D

98 THE PROBLEMS OF PHILOSOPHY

expect food when they see the person who
usually feeds them. We know that all these
rather crude expectations of uniformity are
liable to be misleading. The man who has
fed the chicken every day throughout its life
at last wrings its neck instead, showing that
more refined views as to the uniformity of
nature would have been useful to the chicken.
But in spite of the misleadingness of such
expectations, they nevertheless exist. The
mere fact that something has happened a
certain number of times causes animals and
men to expect that it will happen again.
Thus our instincts certainly cause us to believe
that the sun will rise to-morrow, but we may
be in no better a position than the chicken
which unexpectedly has its neck wrung. We
V'' have therefore to distinguish the fact that
past uniformities cause expectations as to the
future, from the question whether there is
any reasonable ground for giving weight to
such expectations after the question of their
validity has been raised.

The problem we have to discuss is whether
there is any reason for believing in what is'

I

ON INDUCTION 99

called " the uniformity of nature." The
belief in the uniformity of nature is the belief
that everything that has happened or will
happen is an instance of some general law
to which there are no exceptions. The crude
expectations which we have been considering
are all subject to exceptions, and therefore
liable to disappoint those who entertain them.
But science habitually assumes, at least as
a working hypothesis, that general rules
which have exceptions can be replaced by
general rules which have no exceptions.
" Unsupported bodies in air fall " is a general
rule to which balloons and aeroplanes are
exceptions. But the laws of motion and the
law of gravitation, which account for the
fact that most bodies fall, also account for
the fact that balloons and aeroplanes can rise ;
thus the laws of motion and the law of gravi-
tation are not subject to these exceptions.

The belief that the sun will rise to-morrow
might be falsified if the earth came suddenly
into contact with a large body which destroyed
its rotation ; but the laws of motion and the
law of gravitation would not be infringed by

100 THE PROBLEMS OF PHILOSOPHY

such an event. The business of science is to
find uniformities, such as the laws of motion
and the law of gravitation, to which, so far
as our experience extends, there are lio ex-
ceptions. In this search science has been
remarkably successful, and it may be conceded
that such uniformities have held hitherto.
This brings us back to the question : Have
we any reason, assuming that they have
always held in the past, to suppose that they
will hold in the future ?

It has been argued that we have reason to
know that the future will resemble the past,
because what was the future has constantly
become the past, and has always been found
to resemble the past, so that we really have
experience of the future, namely of times
which were formerly future, which we may
call past futures. But such an argument
really begs the very question at issue. We
have experience of past futures, but not of
future futures, and the question is : Will future
•^/futures resemble past futures ? This ques-
tion is not to be answered by an argument
which starts from past futures alone. We

I

I

ON INDUCTION 101

have therefore still to seek for some principle
which shall enable us to know that the future
will follow the same laws as the past.

The reference to the future in this question
is not essential. The same question arises
when we apply the laws that work in our
experience to past things of which we have
no experience — as, for example, in geology,
or in theories as to the origin of the Solar
System. The question we really have to ask v^
is : " When two things have been found to be
often associated, and no instance is known
of the one occurring without the other, does \
the occurrence of one of the two, in a fresh
instance, give any good ground for expecting
the other ? " On our answer to this question
must depend the validity of the whole of our
expectations as to the future, the whole of
the results obtained by induction, and in fact
practically all the beliefs upon which our
daily life is based.

It must be conceded, to begin with, that'^'
the fact that two things have been found often
together and never apart does not, by itself,
suffice to yrove demonstratively that they

102 THE PROBLEMS OF PHILOSOPHY

will be found together in the next case we
examine. The most we can hope is that the
oftener things are found together, the more
probable it becomes that they will be found
together another time, and that, if they have
been found together ofte • enough, the prob-
ability will amount almos t^c certainty. It
can never quite reach cer'ahity, because we
know that in spite of frequent repetitions
there sometimes is a failure at the last, as
in the case of the chicken whose neck is wrung.
Thus probability is all we ought to seek.

It might be urged, as against the view we
are advocating, that we know all natural
phenomena to be subject to the reign of law,
and that sometimes, on the basis of observa-
tion, we can see that only one law can possibly
fit the facts of the case. Now to this view
there are two answers. The first is that,
even if some law which has no exceptions
applies to our case, we can never, in practice,
be sure that we have discovered that law and
not one to which there are exceptions. The
second is that the reign of law would seem to
be itself only probable, and that our belief

I

ON INDUCTION 108

that it will hold in the future, or in unexamined
eases in the past, is itself based upon the very-
principle we are examining.

The principle we are examining may be ^'
called the principle of induction, and its two
parts may be 1 as follows :

(a) When a t)\\ ^J^ of a certain sort A has
been found to be associated with a thing of a
certain other sort B, and has never been found
dissociated from a thing of the sort B, the
greater the number of cases in which A and B
have been associated, the greater is the
probability that they will be associated in a
fresh case in which one of them is known to
be present ;

(b) Under the same circumstances, a suffi-
cient number of cases of association will make
the probability of a fresh association nearly
a certainty, and will make it approach cer-
tainty without limit.

As just stated, the principle applies only to
the verification of our expectation in a single
fresh instance. But we want also to know
that there is a probability in favour of the
general law that things of the sort A are

104 THE PROBLEMS OF PHILOSOPHY

always associated with things of the sort B,
provided a sufficient number of cases of
association are known, and no cases of failure
of association are known. The probabiHty of
the general law is obviously less than the
probability of the particular case, since if
the general law is true, the particular case
must also be true, whereas the particular
ease may be true without the general law being
true. Nevertheless the probability of the
general law is increased by repetitions, just
as the probability of the particular case is.
v^We may therefore repeat the two parts of
our principle as regards the general law,
thus :

(a) The greater the number of cases in
which a thing of the sort A has been found
associated with a thing of the sort B, the more
probable it is (if no cases of failure of associa-
tion are known) that A is always associated
with B ;

(h) Under the same circumstances, a suffi-
cient number of cases of the association of
A with B will make it nearly certain that A
is always associated with B, and will make

I

ON INDUCTION 105

this general law approach certainty without
limit.

It should be noted that probability is ^^
always relative to certain data. In our case,
the data are merely the known cases of co-
existence of A and B, There may be other
data, which might be taken into account,
which would gravely alter the probability.
For example, a man who had seen a great
many white swans might argue, by our prin-
ciple, that on the data it was probable that all
swans were white, and this might be a per-
fectly sound argument. The argument is
not disproved by the fact that some swans
are black, because a thing may very well
happen in spite of the fact that some data
render it improbable. In the case of the
swans, a man might know that colour is a
very variable characteristic in many species
of animals, and that, therefore, an induction
as to colour is peculiarly liable to error.
But this knowledge would be a fresh datum,
by no means proving that the probability
relatively to our previous data had been
wrongly estimated, y^he fact, therefore, that

M

106 THE PROBLEMS OF PHILOSOPHY

things often fail to fulfil our expectations
is no evidence that our expectations will not
'probably be fulfilled in a given case or a given

'^ class of cases. Thus our inductive principle
is at any rate not capable of being disproved
by an appeal to experience.

i/ The inductive principle, however, is equally
incapable of being proved by an appeal to
experience. Experience might conceivably
confirm the inductive principle as regards the
cases that have been already examined ; but
as regards unexamined cases, it is the in-
ductive principle alone that can justify any
inference from what has been examined to
what has not been examined. All arguments
which, on the basis of experience, argue as
to the future or the unexperienced parts of the ]
past or present, assume the inductive prin-
' ciple ; hence we can never use experience to
prove the inductive principle without begging
the question. Thus we mu«t either accept
the inductive principle on the ground of its
intrinsic evidence, or forgo all justification
of our expectations about the future. If the
principle is unsound, we have no reason to

ON INDUCTION 107

expect the sun to rise to-morrow, to expect
bread to be more nourishing than a stone, or
to expect that if we throw ourselves off the
roof we shall fall. When we see what looks
like our best friend approaching us, we shall
have no reason to suppose that his body is
not inhabited by the mind of our worst enemy
or of some total stranger. All our conduct is
ha^;^^-upnr> associations which have worked '
in the past, and which we therefore regard as
IjMy to work in the future ; and this lil?:£li-
l^JOoa2lOE^^^^^^^^^^~^^i^?^^i^^y..^^ the
inductive prijigiplg. - - .-t:.. ,^^

'""the general principles of science, such as
the belief in the reign of law, and the belief
that every event must have a cause, are as
completely dependent upon the inductive
principle as are the beliefs of daily life. All
such general principles are believed because
mankind have found innumerable instances of
their truth, and no instances of their false-
hood. But this affords no evidence for their
truth in the future, unless the inductive
principle is assumed.
Thus all knowledge which, on a basis of •^

108 THE PROBLEMS OF PHILOSOPHY

experience, tells us something about what is
not experienced, is based upon a belief which
experience can neither confirm nor confute,
yet which, at least in its more concrete appli-
cations, appears to be as firmly rooted in us
as many of the facts of experience. The
existence and justification of such beliefs —
for the inductive principle, as we shall see,
is not the only example — raises some of the
most difficult and most debated problems of
philosophy. We will, in the next chapter,*^
consider briefly what may be said to account
for such knowledge, and what is its scope and
its degree of certainty.

CHAPTER VII

ON OUR KNOWLEDGE OF GENERAL PRINCIPLES

We saw in the preceding chapter that>^
the principle of induction, while necessary
to the validity of all arguments based on
experience, is itself not capable of being
proved by experience, and yet is unhesitat-
ingly believed by every one, at least in all its
concrete applications. In these character-
istics the principle of induction does not stand
alone. There are a number of other prin-'^
eiples which cannot be proved or disproved by
experience, but are used in arguments which
start from what is experienced.

Some of these principles have even greater*''
evidence than the principle of induction,
and the knowledge of them has the same
degree of certainty as the knowledge of the
existence of sense-data. They constitute the
109

110 THE PROBLEMS OF PHILOSOPHY!

means of drawing inferences from what ist
given in sensation ; and if what we infer is]
to be true, it is just as necessary that our|
principles of inference should be true as iti
is that our data should be true. The^ prin-
ciples of inference are apt to be overlooked
because of their very obviousness — the as-
sumption involved is assented to without our
realising that it is an assumption. But it is
'' very important to realise the use of principles
' of inference, if a correct theory of knowledge
is to be obtained ; for our knowledge of them
raises interesting and difficult questions.

In all our knowledge of general principles,
what actually happens is that first of all we
realise some particular application of the
principle, and then we realise that the particu-
larity is irrelevant, and that there is a generality;
which may equally truly be affirmed. This
is of course familiar in such matters as teach-
ing arithmetic : " two and two are four " is
first learnt in the case of some particular pair
of couples, and then in some other particular
case, and so on, until at last it becomes possible
to see that it is true of any pair of couples.

i

GENERAL PRINCIPLES 111

The same thing happens with logical prin-
ciples. Suppose two men are discussing
what day of the month it is. One of them
says, "At least you will admit that if yester-
day was the 15th to-day must be the 16th."
"Yes," says the other, "I admit that."
" And you know," the first continues, "that
yesterday was the 15th, because you dined
with Jones, and your diary will tell you that
was on the 15th." " Yes," says the second ;
" therefore to-day is the 16th."

Now such an argument is not hard to follow ;
and if it is granted that its premisses are true
in fact, no one will deny that the conclusion
must also be true. But it depends for its
truth upon an instance of a general logical
principle. The logical principle is as follows :
" Suppose it known that if this is true, then
that is true. Suppose it also known that this
is true, then it follows that that is true."
When it is the case that if this is true, that
is true, we shall say that this " implidfe " that,
and that that "follows from" this. Thus
our principle states that if this implies that,
and this is true, then that is true. In other

112 THE PROBLEMS OF PHILOSOPHY

words, " anything implied by a tnie pro-
position is true," or " whatever follows from
a true proposition is true."
1^ This principle is really involved — at least,
concrete instances of it are involved — in all
demonstrations. Whenever one thing which
we believe is used to prove something else,
which we consequently believe, this principle
is relevant. If any one asks : " Why
should I accept the results of valid arguments
based on true premisses ? " we can only
answer by appealing to our principle. In
fact, the truth of the principle is impossible
to doubt, and its obviousness is so great that
at first sight it seems almost trivial. Such
principles, however, are not trivial to the
,A philosopher, for they show that we may have
indubitable knowledge which is in no way
derived from objects of sense.
J The above principle is merely one of a
certain number of self-evident logical prin-
ciples. Some at least of these principles must
be granted before any argument or proof
becomes possible. When some of them have
been granted, others can be proved, though

»

GENERAL PRINCIPLES 113

these others, so long as they are simple, are
just as obvious as the principles taken for
granted. For no very good reason, three of
these principles have been singled out by
tradition under the name of " Laws of
Thought."

They are as follows :

(1) The law of identity: "Whatever is,
is."

(2) The law of contradiction : *' Nothing
can both be and not be."

(3) The law of excluded middle : " Every-
thing must either be or not be."

These three laws are samples of self-evident
logical principles, but are not really more
fundamental or more self-evident than various
other similar principles : for instance, the one
we considered just now, which states that
what follows from a true premiss is true.
The name " laws of thought " is also mis-
leading, for what is important is not the fact|
that we think in accordance with these laws,
but the fact that things behave in accordance
with them ; in other words, the fact that when
we think in accordance with them we think

114 THE PROBLEMS OF PHILOSOPHY

truly. But this is a large question, to which
we must return at a later stage.
1/ In addition to the logical principles which
enable us to prove from a given premiss that
something is certainly true, there are other
logical principles which enable us to prove,
fron; a given premiss, that there is a greater
or less probability that something is true.
An example of such principles — perhaps the
most important example — is the inductive
principle, which we considered in the pre-
ceding chapter.

- One of the great historic controversies in
philosophy is the controversy between the
two schools called respectively "empiricists "
and " rationalists." The empiricists — ^who
are best represented by the British philo-
sophers, Locke, Berkeley, and Hume — main-
tained that all our knowledge is derived from
experience ; the rationalists — who are repre-
sented by the Continental philosophers of the
seventeenth century, especially Descartes and
Leibniz, maintained that, in addition to
what we know by experience, there are certain
'' innate ideas " and " innate principles,"

GENERAL PRINCIPLES 115

which we know independently of experience.
It has now become possible to decide with
some confidence as to the truth or falsehood of
these opposing schools. It must be admitted,
for the reasons already stated, that logical
principles are known to us, and cannot be
themselves proved by experience, since all
proof presupposes them. In this, therefore,
which was the most important point of the
controversy, the rationalists were in the
right.

On the other hand, even that part of our
knowledge which is logically independent of
experience (in the sense that experience can-
not prove it) is yet elicited and caused by
experience. It is on occasion of particular ex-'
periences that we become aware of the general
laws which their connections exemplify.
It would certainly be absurd to suppose that
there are innate principles in the sense that
babies are born with a knowledge of every-
thing which men know and which cannot be
deduced from what is experienced. For this
reason, the word " innate " would not now
be employed to describe our knowledge of

/

116 THE PROBLEMS OF PHILOSOPHY

logical principles. The phrase " a pn'on* " is
less objectionable, and is more usual in modern
writers. Thus, while admitting that all know-
ledge is elicited and caused by experience, we
shall nevertheless hold that some knowledge
is a priori, in the sense that the experience
which makes us think of it does not suffice to
prove it, but merely so directs our attention
that we see its truth without requiring any
proof from experience. !

There is another point of great importance,
in which the empiricists were in the right
as against the rationalists. Nothing can be
known to exist except by the help of experi-
ence. That is to say, if we wish to prove
that something of which we have no direct
experience exists, we must have among our
premisses the existence of one or more things
of which we have direct experience. Our
belief that the Emperor of China exists, for
example, rests upon testimony, and testimony
consists, in the last analysis, of sense-data
seen or heard in reading or being spoken
to. Rationalists believed that, from general
consideration as to what must be, they could

GENERAL PRINCIPLES 117

deduce the existence of this or that in the
actual world. In this belief they seem to
have been mistaken. All the knowledge that
we can acquire a priori concerning existence
seems to be hypothetical : it tells us that if
one thing exists, another must exist, or, more
generally, that if one proposition is true,
another must be true. This is exemplified by
the principles we have already dealt with, such
as " */ this is true, and this implies that, then
that is true," or " if this and that have been
repeatedly found connected, they will prob-
ably be connected in the next instance in
which one of them is found." Thus the scope
and power of a priori principles is strictly
limited. All knowledge that something exists 0^ y
must be in part dependent on experience. "'''
When anything is known immediately, its
existence is known by experience alone ; when .
anything is proved to exist, without being
known immediately, both experience and a \
priori principles must be required in the proof. ,
Knowledge is called empirical when it rests
wholly or partly upon experience. Thus all
knowledge which asserts existence is empirical.

118 THE PROBLEMS OF PHILOSOPHY

and the only a ^priori knowledge concerning
existence is hypothetical, giving connections
among things that exist or may exist, but
not giving actual existence.

A priori knowledge is not all of the logical
kind we have been hitherto considering.
Perhaps the most important example of non-
logical a priori knowledge is knowledge as to
ethical value. I am not speaking of judg-
ments as to what is useful or as to what is
virtuous, for such judgments do require
empirical premisses ; I am speaking of judg-
ments as to the intrinsic desirability of things.
If something is useful, it must be useful because
is secures some end ; the end must, if we have
gone far enough, be valuable on its own ac-
count, and not merely because it is useful for
some further end. Thus all judgments as
to what is useful depend upon judgments as
to what has value on its own account.

We judge, for example, that happiness is
more desirable than misery, knowledge than
ignorance, goodwill than hatred, and so on.
Such judgments must, in part at least, be
immediate and a priori. Like our previous

GENERAL PRINCIPLES 119

a priori judgments, they may be elicited by
experience, and indeed they must be ; for it
seems not possible to judge whether anything
is intrinsically valuable unless we have
experienced something of the same kind.
But it is fairly obvious that they cannot be
'proved by experience ; for the fact that a
thing exists or does not exist cannot prove
either that it is good that it should exist or
that it is bad. The pursuit of this subject
belongs to ethics, where the impossibility
of deducing what ought to be from what is
has to be established. In the present con-
nection, it is only important to realise that
knowledge as to what is intrinsically of value
is a priori in the same sense in which logic, jl
is a priori, namely in the sense that the truth I
of such knowledge can be neither proved nor ul
disproved by experience. i

All pure mathematics is a priori, like logic.
This was strenuously denied by the empirical
philosophers, who maintained that experience
was as much the source of our knowledge of
arithmetic as of our knowledge of geography.
They maintained that by the repeated ex-

120 THE PROBLEMS OF PHILOSOPHY

perience of seeing two things and two other
things, and finding that altogether they made
four things, we were led by induction to the
conclusion that two things and two other
things would always make four things alto-
gether. If, however, this were the source of
our knowledge that two and two are four,
we should proceed differently, in persuading
ourselves of its truth, from the way in which
we do actually proceed. In fact, a certain
number of instances are needed to make us
think of two abstractly, rather than of two
coins or two books or two people, or two of
any other specified kind. But as soon as we
are able to divest our thoughts of irrelevant
particularity, we become able to see the
general principle that two and two are four ;
any one instance is seen to be typical, and the
examination of other instances becomes un-
necessary.*

The same thing is exemplified in geometry.
If we want to prove some property of all
triangles, we draw some one triangle and

* Cf. A. N. Whitehead, Introduction to Mathematics
(Home University Library)*

GENERAL PRINCIPLES 121

reason about it ; but we can avoid making
use of any property which it does not share
with all other triangles, and thus, from our
particular case, we obtain a general result.
We do not, in fact, feel our certainty that
two and two are four increased by fresh
instances, because, as soon as we have seen
the truth of this proposition, our certainty
becomes so great as to be incapable of growing
greater. Moreover, we feel some quality of
necessity about the proposition " two and
two are four," which is absent from even the
best attested empirical generalisations. Such
generalisations always remain mere facts :
we feel that there might be a world in which
they were false, though in the actual world
they happen to be true. In any possible
world, on the contrary, we feel that two and
two would be four : this is not a mere fact,
but a necessity to which everything actual
and possible must conform.

The case may be made clearer by con-
sidering a genuinely empirical generalisation,
such as " All men are mortal." It is plain that
we believe this proposition, in the first place.

122 THE PROBLEMS OF PHILOSOPHY

because there is no known instance of men
living beyond a certain age, and in the second
place because there seem to be physiological
grounds for thinking that an organism such
as a man's body must sooner or later wear
out. Neglecting the second ground, and
considering merely our experience of men's
mortality, it is plain that we should not be
content with one quite clearly understood
instance of a man dying, whereas, in the case
of " two and two are four," one instance does
suffice, when carefully considered, to persuade
us that the same must happen in any other
instance. Also we can be forced to admit,
on reflection, that there may be some doubt,
however slight, as to whether all men are
mortal. This may be made plain by the
attempt to imagine two different worlds, in
one of which there are men who are not
mortal, while in the other two and two make
five. When Swift invites us to consider the
race of Struldbugs who never die, we are
able to acquiesce in imagination. But a world
where two and two make five seems quite on
a different level. We feel that such a world, if

GENERAL PRINCIPLES 123

there were one, would upset the whole fabric
of our knowledge and reduce us to utter doubt.
The fact is that, in simple mathematical
judgments such as " two and two are four,"
and also in many judgments of logic, we can
know the general proposition without inferring
it from instances, although some instance is
usually necessary to make clear to us what the
general proposition means. This is why there
is real utility in the process of deduction, which
goes from the general to the general or from
the general to the particular, as well as in the
process of induction, which goes from the par-
ticular to the particular, or from the particular
to the general. It is an old debate among
philosophers whether deduction ever gives
new knowledge. We can now see that in
certain cases, at least, it does do so. If we-
already know that two and two always make
four, and we know that Brown and Jones are
two, and so are Robinson and Smith, we can
deduce that Brown and Jones and Robinson
and Smith are four. This is new knowledge,
not contained in our premisses, because the
general proposition, " two and two are four,'!

124 THE PROBLEMS OF PHILOSOPHY

never told us there were such people as Brown
and Jones and Robinson and Smith, and the
particular premisses did not tell us that there
were four of them, whereas the particular
proposition deduced does tell us both these
things.

But the newness of the knowledge is much
less certain if we take the stock instance of
deduction that is always given in books on
logic, namely, " All men are mortal ; Socrates
is a man, therefore Socrates is mortal."
In this case, what we really know beyond
reasonable doubt is that certain men, A,
B, C, were mortal, since, in fact, they have
died. If Socrates is one of these men, it is
foolish to go the roundabout way through
" all men are mortal " to arrive at the con-
clusion that probably Socrates is mortal. If
Socrates is not one of the men on whom our
induction is based, we shall still do better to
argue straight from our A, B, C, to Socrates,
than to go round by the general proposition,
" all men are mortal." For the probability
that Socrates is mortal is greater, on our data,
than the probability that all men are mortal.

GENERAL PRINCIPLES 125

(This is obvious, because if all men are mortal,
so is Socrates ; but if Socrates is mortal, it
does not follow that all men are mortal.)
Hence we shall reach the conclusion that
Socrates is mortal with a greater approach to
certainty if we make our argument purely-
inductive than if we go by way of " all men
are mortal " and then use deduction.

This illustrates the difference between
general propositions known a priori, such as
" two and two are four," and empirical
generalisations such as " all men are mortal."
In regard to the former, deduction is the
right mode of argument, whereas in regard to
the latter, induction is always theoretically
preferable, and warrants a greater confidence
in the truth of our conclusion, because all
empirical generalisations are more uncertain
than the instances of them.

We have now seen that there are proposi-
tions known a priori, and that among them are
the propositions of logic and pure mathematics,
as well as the fundamental propositions of
ethics. The question which must next occupy
us is this : How is it possible that there

126 THE PROBLEMS OF PHILOSOPHY

should be such knowledge ? And more par-
ticularly, how can there be knowledge of
general propositions in cases where we have
not examined all the instances, and indeed
never can examine them all, because their
number is infinite ? These questions, which
were first brought prominently forward by
the German philosopher Kant (1724-1804),
are very difficult, and historically very im-
portant.

CHAPTER VIII

HOW A PRIORI KNOWLEDGE IS POSSIBLE

Immanuel Kant is generally regarded as
the greatest of the modern philosophers.
Though he lived through the Seven Years'
War and the French Revolution, he never
interrupted his teaching of philosophy at
Konigsberg in East Prussia. His most dis-
tinctive contribution was the invention of what
he called the " critical " philosophy, which,
assuming as a datum that there is knowledge
of various kinds, inquired how such know-
ledge comes to be possible, and deduced, from
the answer to this inquiry, many metaphy-
sical results as to the nature of the world.
Whether these results were valid may well be
doubted. But Kant undoubtedly deserves
credit for two things : first, for having per-
ceived that we have a priori knowledge which
127

128 THE PROBLEMS OF PHILOSOPHY

is not purely " analytic," i.e. such that
the opposite would be self -contradictory ;
and secondly, for having made evident the
philosophical importance of the theory of
knowledge.

Before the time of Kant, it was generally
held that whatever knowledge was a priori
must be " analytic." What this word means
will be best illustrated by examples. If I
say, " A bald man is a man," " A plane figure
is a figure," " A bad poet is a poet," I make
a purely analytic judgment : the subject
spoken about is given as having at least two
properties, of which one is singled out to be
asserted of it. Such propositions as the above
are trivial, and would never be enunciated in
real life except by an orator preparing the
way for a piece of sophistry. They are called
" analytic " because the predicate is obtained
by merely analysing the subject. Before the
time of Kant it was thought that all judgments
of which we could be certain a priori were
of this kind : that in all of them there was a
predicate which was only part of the subject
of which it was asserted. If this were so, we

d*
t
i
c

1

St

's
r

i

■

A PRIORI KNOWLEDGE 131

some answer. The answer of the pure
empiricists, that our mathematical know-
ledge is derived by induction from particular
instances, we have already seen to be inade-
quate, for two reasons : first, that the validity
of the inductive principle itself cannot be
proved by induction ; secondly, that the
general propositions of mathematics, such as
" two and two always make four," can obvi-
ously be known with certainty by considera-
tion of a single instance, and gain nothing by
enumeration of other cases in which they
have been found to be true. Thus our
knowledge of the general propositions of
mathematics (and the same applies to
logic) must be accounted for otherwise than
our (merely probable) knowledge of em-
pirical generalisations such as " all men are
mortal."

The problem arises through the fact that
such knowledge is general, whereas all ex-
perience is particular. It seems strange that
we should apparently be able to know some
truths in advance about particular things of
which we have as yet no experience ; but it

132 THE PROBLEMS OF PHILOSOPHY

cannot easily be doubted that logic and arith-
metic will apply to such things. We do not
know who will be the inhabitants of London
a hundred years hence ; but we know that
any two of them and any other two of them
will make four of them. This apparent
power of anticipating facts about things of
which we have no experience is certainly
surprising. Kant's solution of the problem,
though not valid in my opinion, is interesting.
It is, however, very difficult, and is differently
understood by different philosophers. We
can, therefore, only give the merest outline
of it, and even that will be thought mis-
leading by many exponents of Kant's
system.

What Kant maintained was that in all our
experience there are two elements to be
distinguished, the one due to the object
(i.e. to what we have called the "physical
object"), the other due to our own nature.
We saw, in discussing matter and sense-
data, that the physical object is different
from the associated sense-data, and that
the sense-data are to be regarded as resulting

A PRIORI KNOWLEDGE 133

from an interaction between the physical
object and ourselves. So far, we are in
agreement with Kant. But what is distinc-
tive of Kant is the way in which he appor-
tions the shares of ourselves and the physical
object respectively. He considers that the
crude material given in sensation — the
colour, hardness, etc. — is due to the object,
and that what we supply is the arrangement
in space and time, and all the relations be-
tween sense-data which result from com-
parison or from considering one as the cause
of the other or in any other way. His
chief reason in favour of this view is that
we seem to have a priori knowledge as to
space and time and causality and compari-
son, but not as to the actual crude material
of sensation. We can be sure, he says,
that anything we shall ever experience
must show the characteristics affirmed of it
in our a priori knowledge, because these
characteristics are due to our own nature,
and therefore nothing can ever come into
our experience without acquiring these
characteristics.

a34 THE PROBLEMS OF PHILOSOPHY

The physical object, which he calls the
*' thing in itself," he regards as essentially
unknowable ; what can be known is the object
as we have it in experience, which he calls
the " phenomenon." The phenomenon, be-
ing a joint product of us and the thing in
itself, is sure to have those characteristics
which are due to us, and is therefore sure to
conform to our a priori knowledge. Hence
this knowledge, though true of all actual and
possible experience, must not be supposed
to apply outside experience. Thus in spite
of the existence of a 'priori knowledge, we
cannot know anything about the thing in
itself or about what is not an actual or possible
object of experience. In this way he tries to
reconcile and harmonise the contentions of
the rationalists with the arguments of the
empiricists.

Apart from minor grounds on which
Kant's philosophy may be criticised, there is
one main objection which seems fatal to any
attempt to deal with the problem of a priori
knowledge by his method. The thing to be
accounted for is our certainty that the facts

A PRIORI KNOWLEDGE 135

must always conform to logic and arithmetic.
To say that logic and arithmetic are contri-
buted by us does not account for this. Our
nature is as much a fact of the existing world
as anything, and there can be no certainty
that it will remain constant. It might happen,
if Kant is right, that to-morrow our nature
would so change as to make two and two
become five. This possibility seems never
to have occurred to him, yet it is one which
utterly destroys the certainty and univer-
sality which he is anxious to vindicate for
arithmetical propositions. It is true that this
possibility, formally, is inconsistent with the
Kantian view that time itself is a form
imposed by the subject upon phenomena,
so that our real Self is not in time and has
no to-morrow. But he will still have to
suppose that the time-order of phenomena
is determined by characteristics of what is
behind phenomena, and this suffices for the
substance of our argument.

Reflection, moreover, seems to make it clear
that, if there is any truth in our arithmetical
beliefs, they must apply to things equally

136 THE PROBLEMS OF PHILOSOPHY

whether we think of them or not. Two
physical objects and two other physical
objects must make four physical objects, even
if physical objects cannot be experienced.
To assert this is certainly within the scope
of what we mean when we state that two and
two are four. Its truth is just as indubitable
as the truth of the assertion that two
phenomena and two other phenomena make
four phenomena. Thus Kant's solution un-
duly limits the scope of a priori propositions,
in addition to failing in the attempt at ex-
plaining their certainty.

Apart from the special doctrines advocated
by Kant, it is very common among philo-
sophers to regard what is a priori as in some
sense mental, as concerned rather with the
way we must think than with any fact of the
outer world. We noted in the preceding
chapter the three principles commonly called
" laws of thought." The view which led to
their being so named is a natural one, but
there are strong reasons for thinking that it
is erroneous. Let us take as an illustra-
tion the law of contradiction. This is

A PRIORI KNOWLEDGE 13T

commonly stated in the form " Nothing
can both be and not be," which is intended
to express the fact that nothing can at once
have and not have a given quaHty. Thus,
for example, if a tree is a beech it cannot
also be not a beech ; if my table is rectan-
gular it cannot also be not rectangular, and
so on.

Now what makes it natural to call this
principle a law of thought is that it is by
thought rather than by outward observation
that we persuade ourselves of its necessary
truth. When we have seen that a tree is a
beech, w^e do not need to look again in order
to ascertain whether it is alsOinot-a-beech^
thought alone makes us know that this is
impossible. But the conclusion that the law
of contradiction is a law of thought is never-
theless erroneous. What we believe, when
we believe the law of contradiction, is not
that the mind is so made that it must believe
the law of contradiction. This belief is a
subsequent result of psychological reflection,
which presupposes the belief in the law of
contradiction. The belief in the law of

133 THE PROBLEMS OF PHILOSOPHY

contradiction is a belief about things, not
only about thoughts. It is not, e.g., the
belief that if we think a certain tree is a
beech, we cannot at the same time think
that it is not a beech ; it is the belief
that if the tree is a beech, it cannot at
the same time be not a beech. Thus the
law of contradiction is about things, and not
merely about thoughts ; and although belief
in the law of contradiction is a thought, the
law of contradiction itself is not a thought,
but a fact concerning the things in the world.
If this, which we believe when we believe the
law of contradiction, were not true of the
things in the world, the fact that we were
compelled to think it true would not save
the law of contradiction from being false ;
and this shows that the law is not a law of
thought.

A similar argument applies to any other
a priori judgment. When we judge that
two and two are four, we are not making a
judgment about our thoughts, but about all
actual or possible couples. The fact that
our minds are so constituted as to believe

I

A PRIORI KNOWLEDGE 139

that two and two are four, though it is true,
is emphatically not what we assert when we
assert that two and two are four. And no
fact about the constitution of our minds
could make it true that two and two are
four. Thus our a priori knowledge, if it
is not erroneous, is not merely knowledge
about the constitution of our minds, but
is applicable to whatever the world may
contain, both what is mental and what is
non-mental.

The fact seems to be that all our a priori
knowledge is concerned with entities which
do not, properly speaking, exist, either in the
mental or in the physical world. These en-
tities are such as can be named by parts of
speech which are not substantives ; they are
such entities as qualities and relations. Sup-
pose, for instance, that I am in my room. I
exist, and my room exists ; but does " in "
exist ? Yet obviously the word " in " has
a meaning ; it denotes a relation which holds
between me and my room. This relation is
something, although we cannot say that it
exists in the same sense in which I and my

140 THE PROBLEMS OF PHILOSOPHY

room exist. The relation " in " is something
which we can think about and understand,
for, if we could not understand it, we could
not understand the sentence " I am in my
room." Many philosophers, following Kant,
have maintained that relations are the work
of the mind, that things in themselves have
no relations, but that the mind brings them
together in one act of thought and thus pro-
duces the relations which it judges them to
have.

This view, however, seems open to objec-
tions similar to those which we urged before
against Kant. It seems plain that it is not
thought which produces the truth of the
proposition " I am in my room." It may be
true that an earwig is in my room, even if
neither I nor the earwig nor any one else is
aware of this truth ; for this truth concerns
only the earwig and the room, and does not
depend upon anything else. Thus relations,
as we shall see more fully in the next chapter,
must be placed in a world which is neither
mental nor physical. This world is of great
importance to philosophy, and in particular]

I

A PRIORI KNOWLEDGE

141

to the problems of a priori knowledge. In the
next chapter we shall proceed to develop its
nature and its bearing upon the questions
with which we have been dealing.

CHAPTER IX

THE WORLD OF UNIVERSALS

At the end of the preceding chapter we saw
that such entities as relations appear to have
a being which is in some way different from
that of physical objects, and also different
from that of minds and from that of sense-
data. In the present chapter we have to
consider what is the nature of this kind of
being, and also what objects there are that
have this kind of being. We will begin with
the latter question.

The problem with which we are now con-
cerned is a very old one, since it was brought
into philosophy by Plato. Plato's " theory
of ideas " is an attempt to solve this very
problem, and in my opinion it is one of the
most successful attempts hitherto made. The
theory to be advocated in what follows is

142

I
I

THE WORLD OF UNIVERSALS 14S

largely Plato's, with merely such inodifica-
tions as time has shown to be necessary.

The way the problem arose for Plato was
more or less as follows. Let us consider, say,
such a notion as justice. If we ask ourselves
what justice is, it is natural to proceed by
considering this, that, and the other just act,
with a view to discovering what they have in
common. They must all, in some sense,,
partake of a common nature, which will be
found in whatever is just and in nothing else.
This common nature, in virtue of which
they are all just, will be justice itself, the pure
essence the admixture of which with facts of
ordinary life produces the multiplicity of just
acts. Similarly with any other word which
may be applicable to common facts, such as
" whiteness " for example. The word will be
applicable to a number of particular things
because they all participate in a common
nature or essence. This pure essence is what
Plato calls an " idea " or " form." (It must
not be supposed that " ideas," in his sense,
exist in minds, though they may be appre-
hended by minds.) The " idea " justice is not

144 THE PROBLEMS OF PHILOSOPHY

identical with anything that is just : it is some-
thing other than particular things, which
particular things partake of. Not being
particular, it cannot itself exist in the world
of sense. Moreover it is not fleeting or
changeable like the things of sense : it is
eternally itself, immutable and indestructible.
Thus Plato is led to a supra-sensible world,
more real than the common world of sense,
the unchangeable world of ideas, which alone
gives to the world of sense whatever pale
reflection of reality may belong to it. The
truly real world, for Plato, is the world of
ideas ; for whatever we may attempt to say
about things in the world of sense, we can
only succeed in saying that they participate
in such and such ideas, which, therefore,
constitute all their character. Hence it is
easy to pass on into a mysticism. We may
hope, in a mystic illumination, to see the ideas
as we see objects of sense ; and we may
imagine that the ideas exist in heaven.
These mystical developments are very natural,
but the basis of the theory is in logic, and it is
as based in logic that we have to consider it.

THE WORLD OF UNIVERSALS 145

The word " idea " has acquired, in the
course of time, many associations which are
quite misleading when appHed to Plato's
" ideas." We shall therefore use the word
"universal" instead of the word "idea," to
describe what Plato meant. The essence of
the sort of entity that Plato meant is that it
is opposed to the particular things that are
given in sensation. We speak of whatever
is given in sensation, or is of the same nature
as things given in sensation, as a particular ;
by opposition to this, a universal will be any-
thing which may be shared by many parti-
culars, and has those characteristics which,
as we saw, distinguish justice and whiteness
from just acts and white things.

When we examine common words, we
find that, broadly speaking, proper names
stand for particulars, while other sub-
stantives, adjectives, prepositions, and verbs
stand for universals. Pronouns stand for
particulars, but are ambiguous : it is only
by the context or the circumstances that
we know what particulars they stand for.
The word " now " stands for a particular.

146 THE PROBLEMS OF PHILOSOPHY

namely the present moment ; but like pro-
nouns, it stands for an ambiguous particular,
because the present is always changing.

It will be seen that no sentence can be
made up without at least one word which
denotes a universal. The nearest approach
would be some such statement as " I like
this." But even here the word " like " de-
notes a universal, for I may like other things,
and other people may like things. Thus all
truths involve universals, and all knowledge
of truths involves acquaintance with uni-
versals.

Seeing that nearly all the words to be
found in the dictionary stand for universals,
it is strange that hardly anybody except
students of philosophy ever realises that there
are such entities as universals. We do not
naturally dwell upon those words in a sentence
which do not stand for particulars ; and if we
are forced to dwell upon a word which stands
for a universal, we naturally think of it as
standing for some one of the particulars that
come under the universal. When, for example,
we hear the sentence, " Charles I.'s head was

I

THE WORLD OF UNIVERSALS 147

cut off," we may naturally enough think of
Charles I., of Charles I.'s head, and of the
operation of cutting off his head, which are all
particulars ; but we do not naturally dwell
upon what is meant by the word " head " or
the word " cut," which is a universal. We
feel such words to be incomplete and insub-
stantial ; they seem to demand a context
before anything can be done with them.
Hence we succeed in avoiding all notice of
universals as such, until the study of philo-
sophy forces them upon our attention.

Even among philosophers, we may say,
broadly, that only those universals which are
named by adjectives or substantives have been
much or often recognised, while those named
by verbs and prepositions have been usually
overlooked. This omission has had a very
great effect upon philosophy ; it is hardly
too much to say that most metaphysics, since
Spinoza, has been largely determined by it.
The way this has occurred is, in outline, as
follows : Speaking generally, adjectives and
common nouns express qualities or properties
of single things, whereas prepositions and

148 THE PROBLEMS OF PHILOSOPHY

verbs tend to express relations between two
or more things. Thus the neglect of pre-
positions and verbs led to the belief that
every proposition can be regarded as attri-
buting a property to a single thing, rather
than as expressing a relation between two or
more things. Hence it was supposed that,
ultimately, there can be no such entities as
relations between things. Hence either there
can be only one thing in the universe, or, if
there are many things, they cannot possibly
interact in any way, since any interaction
would be a relation, and relations are im-
possible.

The first of these views, which was advo-
cated by Spinoza, and is held in our own day
by Mr. Bradley and many other philosophers,
is called monism ; the second, which was
advocated by Leibniz, but is not very common
nowadays, is called monadism, because each
of the isolated things is called a monad. Both
these opposing philosophies, interesting as
they are, result, in my opinion, from an undue
attention to one sort of universals, namely the
sort represented by adjectives and substan-

THE WORLD OF UNIVERSALS 149

tives rather than by verbs and preposi-
tions.

As a matter of fact, if any one were anxious
to deny altogether that there aTe such things
as universals, we should find that we cannot
strictly prove that there are such entities as
qualities, i.e. the universals represented by
adjectives and substantives, whereas we can
prove that there must be relations, i.e. the
sort of universals generally represented by
verbs and prepositions. Let us take in illus-
tration the universal whiteness. If we believe
that there is such a universal, we shall say
that things are white because they have the
quality of whiteness. This view, however,
was strenuously denied by Berkeley and
Hume, w^ho have been followed in this by
later empiricists. The form which their
denial took was to deny that there are such
things as " abstract ideas." When we want
to think of whiteness, they said, we form an
image of some particular white thing, and
reason concerning this particular, taking care
not to deduce anything concerning it which
we cannot see to be equally true of any other

150 THE PROBLEMS OF PHILOSOPHY

white thing. As an account of our actual
mental processes, this is no doubt largely-
true. In geometry, for example, when we
wish to prove something about all triangles,
we draw a particular triangle and reason about
it, taking care not to use any characteristic
which it does not share with other triangles.
The beginner, in order to avoid error, often
finds it useful to draw several triangles, as
unlike each other as possible, in order to
make sure that his reasoning is equally applic-
able to all of them. But a difficulty emerges
as soon as we ask ourselves how we know
that a thing is white or a triangle. If we
wish to avoid the universals whiteness and
triangularity, we shall choose some particular
patch of white or some particular triangle,
and say that anything is white or a triangle
if it has the right sort of resemblance to our
chosen particular. But then the resemblance
required will have to be a universal. Since
there are many white things, the resemblance
must hold between many pairs of particular
w^hite things ; and this is the characteristic
of a universal. It will be useless to say that

THE WORLD OF UNIVERSALS 151

there is a different resemblance for each
pair, for then we shall have to say that these
resemblances resemble each other, and thus
at last we shall be forced to admit resem-
blance as a universal. The relation of re-
semblance, therefore, must be a true universal. X
And having been forced to admit this uni-
versal, we find that it is no longer worth
while to invent difficult and unplausible
theories to avoid the admission of such
universals as whiteness and triangularity.

Berkeley and Hume failed to perceive
this refutation of their rejection of " abstract
ideas," because, like their adversaries, they
only thought of qualities, and altogether
ignored relations as universals. We have
therefore here another respect in which the
rationalists appear to have been in the right
as against the empiricists, although, owing
to the neglect or denial of relations, the
deductions made by rationalists were, if any-
thing, more apt to be mistaken than those
made by empiricists.

Having now seen that there must be such
entities as universals, the next point to be

■

152 THE PROBLEMS OF PHILOSOPHY

proved is that their being is not merely mental.
By this is meant that whatever being belongs
to them is independent of their being thought
of or or in any way apprehended by minds.
We have already touched on this subject at
the end of the preceding chapter, but we
must now consider more fully what sort of
being it is that belongs to universals.

Consider such a proposition as " Edinburgh
is north of London." Here we have a re-
lation between two places, and it seems plain
that the relation subsists independently of
our knowledge of it. When we come to know
that Edinburgh is north of London, we come
to know something which has to do only with
Edinburgh and London : we do not cause the
truth of the proposition by coming to know
it, on the contrary we merely apprehend a
fact which was there before we knew it. The
part of the earth's surface where Edinburgh
stands would be north of the part where
London stands, even if there were no human
being to know about north and south, and
even if there were no minds at all in the
universe. This is, of course, denied by. many

THE WORLD OF UNIVERSALS 153;

philosophers, either for Berkeley's reasons
or for Kant's. But we have already con-
sidered these reasons, r.nd decided that they
are inadequate. We may therefore now
assume it to be true that nothing mental is
presupposed in the fact that Edinburgh is
north of London. But this fact involves the
relation " north of," which is a universal ;
and it would be impossible for the whole fact to
involve nothing mental if the relation " north
of," which is a constituent part of the fact,
did involve anything mental. Hence we
must admit that the relation, like the terms
it relates, is not dependent upon thought, but
belongs to the independent world which
thought apprehends but does not create.

This conclusion, however, is met by the
difficulty that the relation " north of " does
not seem to exist in the same sense in which
Edinburgh and London exist. If we ask
" Where and when does this relation exist ? "
the answer must be " Nowhere and no when."
There is no place or time where we can find
the relation " north of." It does not exist in
Edinburgh any more than in London, for it

154 THE PROBLEMS OF PHILOSOPHY

relates the two and is neutral as between
them. Nor can we say that it exists at any-
particular time. Now everything that can
be apprehended by the senses or by intro-
spection exists at some particular time.
Hence the relation " north of " is radically
different from such things. It is neither
in space nor in time, neither material nor
mental ; yet it is something.

It is largely the very peculiar kind of
being that belongs to universals which has led
many people to suppose that they are really
mental. We can think of a universal, and our
thinking then exists in a perfectly ordinary
sense, like any other mental act. Suppose, for
example, that we are thinking of whiteness.
Then in one sense it may be said that white-
ness is "in our mind." We have here the
same ambiguity as we noted in discussing
Berkeley in Chapter IV. In the strict sense,
it is not whiteness that is in our mind, but the
act of thinking of whiteness. The connected
ambiguity in the word " idea," which we
noted at the same time, also causes confusion
here. In one sense of this word, namely the

THE WORLD OF UNIVERSALS 155

sense in which it denotes the object of an act
of thought, whiteness is an " idea." Hence,
if the ambiguity is not guarded against, we
may come to think that whiteness is an
" idea " in the other sense, i.e, an act of
thought ; and thus we come to think that
whiteness is mental. But in so thinking, we
rob it of its essential quality of universality.
One man's act of thought is necessarily a
different thing from another man's ; one
man's act of thought at one time is neces-
sarily a different thing from the same man's
act of thought at another time. Hence, if
whiteness were the thought as opposed to its
object, no two different men could think of it,
and no one man could think of it twice.
That which many different thoughts of white-
ness have in common is their object, and this
object is different from all of them. Thus
universals are not thoughts, though when
known they are the objects of thoughts.

We shall find it convenient only to speak
of things existing when they are in time, that
is to say, when we can point to some time ai
which they exist (not excluding the possi-

156 THE PROBLEMS OF PHILOSOPHY

bility of their existing at all times). Thus
thoughts and feelings, minds and physical
objects exist. But universals do not exist
in this sense ; we shall say that they subsist
or have being, where " being " is opposed to
" existence " as being timeless. The world
of universals, therefore, may also be described
as the world of being. The world of being
is unchangeable, rigid, exact, delightful to
the mathematician, the logician, the builder
of metaphysical systems, and all who love
perfection more than life. The world of
existence is fleeting, vague, without sharp
boundaries, without any clear plan or arrange-
ment, but it contains all thoughts and feelings,
all the data of sense, and all physical objects,
everything that can do either good or harm,
everything that makes any difference to the
value of life and the world. According to
our temperaments, we shall prefer the con-
templation of the one or of the other. The
one we do not prefer will probably seem to us
a pale shadow of the one we prefer, and hardly
worthy to be regarded as in any sense real.
But the truth is that both have the same

THE WORLD OF UNIVERSALS 157

claim on our impartial attention, both are
real, and both are important to the meta-
physician. Indeed no sooner have we dis-
tinguished the two worlds than it becomes
necessary to consider their relations.

But first of all we must examine our
knowledge of universals. This consideration,
will occupy us in the following chapter,
where we shall find that it solves the problem
of a priori knowledge, from which we were
first led to consider universals.

CHAPTER X

ON OUR KNOWLEDGE OF UNIVERSALS

In regard to one man's knowledge at a
given time, universals, like particulars, may-
be divided into those known by acquaintance,
those known only by description, and those
not known either by acquaintance or by de-
scription.

Let us consider first the knowledge of
universals by acquaintance. It is obvious,
to begin with, that we are acquainted with
such universals as white, red, black, sweet,
sour, loud, hard, etc., ix. with qualities
which are exemplified in sense-data. When
we see a white patch, we are acquainted,
in the first instance, with the particular
patch ; but by seeing many white patches,
we easily learn to abstract the whiteness
which they all have in common, and in

158

ON KNOWLEDGE OF UNIVERSALS 159

learning to do this we are learning to be
acquainted with whiteness. A similar pro-
cess will make us acquainted with any
other universal of the same sort. Universals
of this sort may be called " sensible quali-
ties." They can be apprehended with less
effort of abstraction than any others, and
they seem less removed from particulars
than other universals are.

We come next to relations. The easiest
relations to apprehend are those which hold
between the different parts of a single complex
sense-datum. For example, I can see at a
glance the whole of the page on which I am
writing ; thus the whole page is included in
one sense-datum. But I perceive that some
parts of the page are to the left of other parts,
and some parts are above other parts. The
process of abstraction in this case seems to
proceed somewhat as follows : I see success-
ively a number of sense-data in which one
part is to the left of another ; I perceive, as in
the case of different white patches, that all
these sense-data have something in com-
mon, and by abstraction I find that what

160 THE PROBLEMS OF PHILOSOPHY

they have in common is a certain relation
between their parts, namely the relation
which I call " being to the left of." In
this way I become acquainted with the
universal relation.

In like manner I become aware of the
relation of before and after in time. Suppose
I hear a chime of bells : when the last bell of
the chime sounds, I can retain the whole
chime before my mind, and I can perceive
that the earlier bells came before the later
ones. Also in memory I perceive that
what I am remembering came before the
present time. From either of these sources
I can abstract the universal relation of be-
fore and after, just as I abstracted the
universal relation "being to the left of."
Thus time - relations, like space - relations,
are among those with which we are ac-
quainted.

Another relation with which we become
acquainted in much the same way is resem-
blance. If I see simultaneously two shades
of green, I can see that they resemble each
other ; if I also see a shade of red at the same

ON KNOWLEDGE OF UNIVERSALS 161

time, I can see that the two greens have
more resemblance to each other than either
has to the red. In this way I become
acquainted with the universal resemblance or
similarity.

Between universals, as between parti-
culars, there are relations of which we may be
immediately aware. We have just seen that
we can perceive that the resemblance between
two shades of green is greater than the re-
semblance between a shade of red and a shade
of green. Here we are dealing with a relation,
namely " greater than," between two re-
lations. Our knowledge of such relations,
though it requires more power of abstraction
than is required for perceiving the qualities
of sense-data, appears to be equally immediate,
and (at least in some cases) equally indubit-
able. Thus there is immediate knowledge
concerning universals as well as concerning
sense-data.

Returning now to the problem of a priori
knowledge, which we left unsolved when we
began the consideration of universals, we find
ourselves in a position to deal with it in a

162 THE PROBLEMS OF PHILOSOPHY

much more satisfactory manner than was
possible before. Let us revert to the pro-
position " two and two are four." It is
fairly obvious, in view of what has been
said, that this proposition states a relation
between the universal "two" and the uni-
versal "four." This suggests a proposition
which we shall now endeavour to esta-
blish ; namely, All a. priori knowledge deals
exclusively with the relations of universals.
This proposition is of great importance,
and goes a long way towards solving our
previous difficulties concerning a 'priori know-
ledge.

The only case in which it might seem, at
first sight, as if our proposition were untrue,
is the case in which an a priori proposition
states that all of one class of particulars
belong to some other class, or (what comes to
the same thing) that all particulars having
some one property also have some other. In
this case it might seem as though we were
dealing with the particulars that have the
property rather than with the property. The
proposition " two and two are four II is really

ON KNOWLEDGE OF UNIVERSALS 163

a case in point, for this may be stated in the
form " any two and any other two are four,"
or " any collection formed of two twos is a
collection of four." If we can show that
such statements as this really deal only with
universals, our proposition may be regarded
as proved.

One way of discovering what a proposition
deals with is to ask ourselves what words we
must understand — in other words, what ob-
jects we must be acquainted with — in order
to see what the proposition means. As soon
as we see what the proposition means, even
if we do not yet know whether it is true
or false, it is evident that we must have
acquaintance with whatever is really dealt
with by the proposition. By applying this
test, it appears that many propositions
which might seem to be concerned with par-
ticulars are really concerned only with uni-
versals. In the particular case of " two and
two are four," even when we interpret it as
meaning " any collection formed of two twos
is a collection of four," it is plain that we
can understand the proposition, i.e, we can

164 THE PROBLEMS OF PHILOSOPHY

see what it is that it asserts, as soon as we
know what is meant by " collection " and
" two " and " four." It is quite unnecessary
to know all the couples in the world : if it
were necessary, obviously we could never
understand the proposition, since the couples
are infinitely numerous and therefore cannot
all be known to us. Thus although our general
statement implies statements about parti-
cular couples, as soon as we know that there are
such particular couples, yet it does not itself
assert or imply that there are such particular
couples, and thus fails to make any statement
whatever about any actual particular couple.
The statement made is about "couple,"
the universal, and not about this or that
couple.

Thus the statement " two and two are four "
deals exclusively with universals, and therefore
may be known by anybody who is acquainted
with the universals concerned and can per-
ceive the relation between them which the
statement asserts. It must be taken as a
fact, discovered by reflecting upon our know-
ledge, that we have the power of sometimes

ON KNOWLEDGE OF UNIVERSALS 165

perceiving such relations between universals,
and therefore of sometimes knowing general
a priori propositions such as those of arith-
metic and logic. The thing that seemed
mysterious, when we formerly considered such
knowledge, was that it seemed to anticipate
and control experience. This, however, we
can now see to have been an error. No fact
concerning anything capable of being ex-
perienced can be known independently of
experience. We know a priori that two things
and two other things together make four
things, but we do not know a priori that if
Brown and Jones are two, and Robinson and
Smith are two, then Brown and Jones and
Robinson and Smith are four. The reason is
that this proposition cannot be understood
at all unless we know that there are such
people as Brown and Jones and Robinson
and Smith, and this we can only know by
experience. Hence, although our general
proposition is a priori, all its applications
to actual particulars involve experience and
therefore contain an empirical element. In
this way what seemed mysterious in our a

166 THE PROBLEMS OF PHILOSOPHY

priori knowledge is seen to have been based
upon an error.

It will serve to make the point clearer if we
contrast our genuine a priori judgment with an
empirical generalisation, such as "all men are
mortals." Here as before, we can understand
what the proposition means as soon as we
understand the universals involved, namely
man and mortal. It is obviously unnecessary
to have an individual acquaintance with the
whole human race in order to understand
what our proposition means. Thus the dif-
ference between an a priori general propo-
sition and an empirical generalisation does
not come in the meaning of the proposition ;
it comes in the nature of the evidence for it.
In the empirical case, the evidence consists
in the particular instances. We believe
that all men are mortal because we know
that there are innumerable instances of men
dying, and no instances of their living be-
yond a certain age. We do not believe it
because we see a connection between the
universal man and the universal mortal. It
is true that if physiology can prove, assum-

ON KNOWLEDGE OF UNIVERSALS 167

ing the general laws that govern living bodies,
that no living organism can last for ever, that
gives a connection between man and mortality
which would enable us to assert our proposi-
tion without appealing to the special evidence
of men dying. But that only means that our
generalisation has been subsumed under a
wider generalisation, for which the evidence
is still of the same kind, though more exten-
sive. The progress of science is constantly
producing such subsumptions, and therefore
giving a constantly wider inductive basis
for scientific generalisations. But although
this gives a greater degree of certainty, it
does not give a different hind : the ultimate
ground remains inductive, i.e. derived from
instances, and not an a priori connection
of universals such as we have in logic and
arithmetic.

Two opposite points are to be observed
concerning a priori general propositions. The
first is that, if many particular instances are
known, our general proposition may be arrived
at in the first instance by induction, and the
connection of universals may be only sub-

168 THE PROBLEMS OF PHILOSOPHY

sequently perceived. For example, it is known
that if we draw perpendiculars to the sides of
a triangle from the opposite angles, all three
perpendiculars meet in a point. It would be
quite possible to be first led to this proposition
by actually drawing perpendiculars in many
cases, and finding that they always met in a
point ; this experience might lead us to look
for the general proof and find it. Such cases
are common in the experience of every mathe-
matician.

The other point is more interesting, and of
more philosophical importance. It is, that
we may sometimes know a general proposition
in cases where we do not know a single in-
stance of it. Take such a case as the following :
We know that any two numbers can be
multiplied together, and will give a third
called their product. We know that all pairs
of integers the product of which is less than
100 have been actually multiplied together,
and the value of the product recorded in the
multiplication table. But we also know that
the number of integers is infinite, and that
only a finite number of pairs of integers ever

I

ON KNOWLEDGE OF UNIVERSALS 169

have been or ever will be thought of by human
beings. Hence it follows that there are pairs
of integers which never have been and never
will be thought of by human beings, and that
all of them deal with integers the product of
which is over 100. Hence we arrive at the
proposition : " All products of two integers,
which never have been and never will be
thought of by any human being, are over 100."
Here is a general proposition of which the
truth is undeniable, and yet, from the very
nature of the case, we can never give an in-
stance ; because any two numbers we may
think of are excluded by the terms of the
proposition.

This possibility, of knowledge of general
propositions of which no instance can be given,
is often denied, because it is not perceived
that the knowledge of such propositions only
requires a knowledge of the relations of uni-
versals, and does not require any knowledge of
instances of the universals in question. Yet
the knowledge of such general propositions
is quite vital to a great deal of what is gener-
ally admitted to be known. For example, we

170 THE PROBLEMS OF PHILOSOPHY

saw, in our early chapters, that physical
objects, as opposed to sense-data, are only
obtained by an inference, and are not things
with which we are acquainted. Hence we
can never know any proposition of the form
" this is a physical object," where " this " is
something immediately known. It follows
that all our knowledge concerning physical
objects is such that no actual instance can be
given. We can give instances of the associ-
ated sense-data, but we cannot give instances
of the actual physical objects. Hence our
knowledge as to physical objects depends
throughout upon this possibility of general
knowledge where no instance can be given.
And the same applies to our knowledge of
other people's minds, or of any other class of
things of which no instance is knov»^n to us by
acquaintance.

We may now take a survey of the sources
of our knowledge, as they have appeared
in the course of our analysis. We have
first to distinguish knowledge of things and
knowledge of truths. In each there are two
kinds, one immediate and one derivative.

I

I

ON KNOWLEDGE OF XJNIVERSALS 171

Our immediate knowledge of things, which we
called acquaintance, consists of two sorts,
according as the things known are particulars
or universals. Among particulars, we have
acquaintance with sense-data and (probably)
with ourselves. Among universals, there seems
to be no principle by which we can decide
which can be known by acquaintance, but it
is clear that among those that can be so known
are sensible qualities, relations of space and
time, similarity, and certain abstract logical
universals. Our derivative knowledge of
things, which we call knowledge by descrip-
tion, always involves both acquaintance
with something and knowledge of truths.
Our immediate knowledge of truths may be
called intuitive knowledge, and the truths so
known may be called self-evident truths.
Among such truths are included those which
merely state what is given in sense, and also
certain abstract logical and arithmetical prin-
ciples, end (though with less certainty) some
ethical propositions. Our derivative know-
ledge of truths consists of everything that
we can deduce from self-evident truths

172 THE PROBLEMS OF PHILOSOPHY

by the use of self-evident principles of
deduction.

If the above account is correct, all our know
ledge of truths depends upon our intuitive
knowledge. It therefore becomes important
to consider the nature and scope of intuitive
knowledge, in much the same way as, at an
earlier stage, we considered the nature and
scope of knowledge by acquaintance. But
knowledge of truths raises a further problem,
which does not arise in regard to knowledge
of things, namely the problem of error. Some
of our beliefs turn out to be erroneous, and
therefore it becomes necessary to consider
how, if at all, we can distinguish knowledge
from error. This problem does not arise
with regard to knowledge by acquaintance,
for, whatever may be the object of acquaint-
ance, even in dreams and hallucinations, there
is no error involved so long as we do not go
beyond the immediate object : error can only
arise when we regard the immediate object,
i.e. the sense-datum, as the mark of some
physical object. Thus the problems con-
nected with knowledge of truths are more

y

ON KNOWLEDGE OF UNIVERSALS 173

difficult than those connected with know-
ledge of things. As the first of the problems
connected with knowledge of truths, let us
examine the nature and scope of our intui-
tive judgments.

CHAPTER XI

ON INTUITIVE KNOWLEDGE

There is a common impression that every-
thing that we beheve ought to be capable of
proof, or at least of being shown to be highly
probable. It is felt by many that a belief
for which no reason can be given is an un-
reasonable belief. In the main, this view is
just. Almost all our common beliefs are
either inferred, or capable of being inferred,
from other beliefs which may be regarded as
giving the reason for them. As a rule, the
reason has been forgotten, or has even never
been consciously present to our minds. Few
of us ever ask ourselves, for example, what
reason there is to suppose the food we are just
going to eat will not turn out to be poison.
Yet we feel, when challenged, that a perfectly
good reason could be found, even if we are
174

ON INTUITIVE KNOWLEDGE 175

not ready with it at the moment. And in
this belief we are usually justified.

But let us imagine some insistent Socrates,
who, whatever reason we give him, continues
to demand a reason for the reason. We must
sooner or later, and probably before very long,
be driven to a point where we cannot find any
further reason, and where it becomes almost
certain that no further reason is even theo-
retically discoverable. Starting with the
common beliefs of daily life, we can be driven
backfrom point to point, until we come to some
general principle, or some instance of a general
principle, which seems luminously evident,
and is not itself capable of being deduced
from anything more evident. In most ques-
tions of daily life, such as whether our food is
likely to be nourishing and not poisonous, we
shall be driven back to the inductive principle,
which we discussed in Chapter VI. But be-
yond that, there seems to be no further
regress. The principle itself is constantly used
in our reasoning, sometimes consciously, some-
times unconsciously ; but there is no reasoning
which, starting from some simpler self-evident

176 THE PROBLEMS OF PHILOSOPHY

principle, leads us to the principle of induction
as its conclusion. And the same holds for
other logical principles. Their truth is evident
to us, and nve employ them in constructing
demonstrations ; but they themselves, or at
least some of them, are incapable of
demons*z;ration.

Self-evidence, however, is not confined to
those among general principles which are
incapable of proof. When a certain number
of logical principles have been admitted, the
jest can be deduced from them ; but the
propositions deduced are often just as self-
evident as those that were assumed without
proof. All arithmetic, moreover, can be
deduced from the general principles of logic,
yet the simple propositions of arithmetic,
such as " two and two are four," are just
as self-evident as the principles of logic.

It would seem, also, though this is more
disputable, that there are some self-evident
ethical principles, such as " we ought to
pursue what is good."

It should be observed that, in all cases of
general principles, particular instances, dealing

ON INTUITIVE KNOWLEDGE 177

with familiar things, are more evident than
the general principle. For example, the
law of contradiction states that nothing can
both have a certain property and not have
it. This is evident as soon as it is understood,
but it is not so evident as that a particular
rose which we see cannot be both red and
not red. (It is of course possible, that parts
of the rose may be red and parts not red,
or that the rose may be of a shade of pink
which we hardly know whether to call red
or not ; but in the former case it is plain that
the rose as a whole is not red, while in the
latter case the answer is theoretically definite
as soon as we have decided on a precise de-
finition of " red.") It is usually through
particular instances that we come to be able
to see the general principle. Only those
who are practised in dealing with abstractions
can readily grasp a general principle without
the help of instances.

In addition to general principles, the other
kind of self-evident truths are those imme-
diately derived from sensation. We will call
such truths " truths of perception," and the

178 THE PROBLEMS OF PHILOSOPHY

judgments expressing them we will call
" judgments of perception." But here a
certain amount of care is required in get-
ting at the precise nature of the truths that
are self-evident. The actual sense-data are
neither true nor false. A particular patch of
colour which I see, for example, simply
exists : it is not the sort of thing that is
true or false. It is true that there is such
a patch, true that it has a certain shape and
degree of brightness, true that it is surrounded
by certain other colours. But the patch
itself, like everything else in the world of
sense, is of a radically different kind from
the things that are true or false, and therefore
cannot properly be said to be true. Thus
whatever self-evident truths may be
obtained from our senses must be different
from the sense-data from which they are
obtained.

It would seem that there are two kinds of
self-evident truths of perception, though
perhaps in the last analysis the two kinds
may coalesce. First, there is the kind
which simply asserts the existence of the

ON INTUITIVE KNOWLEDGE 179

sense-datum, without in any way analysing
it. We see a patch of red, and we judge
" there is such-and-such a patch of red," or
more strictly " there is that " ; this is one
kind of intuitive judgment of perception.
The other kind arises when the object of
sense is complex, and we subject it to some
degree of analysis. If, for instance, we see
a round patch of red, we may judge " that
patch of red is round." This is again a
judgment of perception, but it differs from
our previous kind. In our present kind we
have a single sense-datum which has both
colour and shape : the colour is red and
the shape is round. Our judgment analyses
the datum into colour and shape, and then
recombines them by stating that the red
colour is round in shape. Another example
of this kind of judgment is " this is to the
right of that," where " this " and " that "
are seen simultaneously. In this kind of
judgment the sense-datum contains con-
stituents which have some relation to each
other, and the judgment asserts that these
constituents have this relation.

180 THE PROBLEMS OF PHILOSOPHY

Another class of intuitive judgments, ana-
logous to those of sense and yet quite dis-
tinct from them, are judgments of memory.
There is some danger of confusion as to the
nature of memory, owing to the fact that
memory of an object is apt to be accompanied
by an image of the object, and yet the image
cannot be what constitutes memory. This
is easily seen by merely noticing that the
image is in the present, whereas what is
remembered is known to be in the past. More-
over, we are certainly able to some extent
to compare our image with the object re-
membered, so that we often know, within
somewhat wide limits, how far our image is
accurate ; but this would be impossible,
unless the object, as opposed to the image,
were in some way before the mind. Thus
the essence of memory is not constituted by
the image, but by having immediately before
the mind an object which is recognised as
past. But for the fact of memory in this
sense, we should not know that there evei
was a past at all, nor should we be able to
understand the word " past," any more than

I

I

ON INTUITIVE KNOWLEDGE 181

a man born blind can understand the word
" light." Thus there must be intuitive judg-
ments of memory, and it is upon the*m, ulti-
mately, that all our knowledge of the past
depends.

The case of memory, however, raises a
difficulty, for it is notoriously fallacious, and
thus throws doubt on the trustworthiness of
intuitive judgments in general. This diffi-
culty is no light one. But let us first narrow
its scope as far as possible. Broadly speaking,
memory is trustworthy in proportion to the
vividness of the experience and to its near-
ness in time. If the house next door was
struck by lightning half a minute ago, my
memory of what I saw and heard will be so
reliable that it would be preposterous to
doubt whether there had been a flash at all.
And the same applies to less vivid experiences,
so long as they are recent. I am absolutely
certain that half a minute ago I was sitting
in the same chair in which I am sitting now.
Going backward over the day, I find things
of which I am quite certain, other things of
which I am almost certain, other things of

182 THE PROBLEMS OF PHILOSOPHY

%vhich I can become certain by thought and
by calling up attendant circumstances, and
some things of which I am by no means
certain. I am quite certain that I ate my
breakfast this morning, but if I were as
indifferent to my breakfast as a philosopher
should be, I should be doubtful. As to the
conversation at breakfast, I can recall some
of it easily, some with an effort, some only
with a large element of doubt, and some not
at all. Thus there is a continual gradation
in the degree of self-evidence of what I
remember, and a corresponding gradation in
the trustworthiness of my memory.

Thus the first answer to the difficulty of
fallacious memory is to say that memory
has degrees of self-evidence, and that these
correspond to the degrees of its trustworthi-
ness, reaching a limit of perfect self-evidence
and perfect trustworthiness in our memory
of events which are recent and vivid.

It would seem, however, that there are
cases of very firm belief in a memory which
is wholly false. It is probable that, in these
cases, what is really remembered, in the

ON INTUITIVE KNOWLEDGE 183

sense of being immediately before the mind,
is something other than what is falsely-
believed in, though something generally asso-
ciated with it. George IV. is said to have at
last believed that he was at the battle of
Waterloo, because he had so often said that
he was. In this case, what was immediately
remembered was his repeated assertion ; the
belief in what he was asserting (if it existed)
would be produced by association with the
remembered assertion, and would therefore
not be a genuine case of memory. It would
seem that cases of fallacious memory can
probably all be dealt with in this way, i.e,
they can be shown to be not cases of memory
in the strict sense at all.

One important point about self-evidence
is made clear by the case of memory, and that
is, that self -evidence has degrees: it is not
a quality which is simply present or absent,
but a quality which may be more or less
present, in gradations ranging from absolute
certainty down to an almost imperceptible
faintness. Truths of perception and some of
the principles of logic have the very highest

184 THE PROBLEMS OF PHILOSOPHY

degree of self-evidence ; truths of immediate
memory have an almost equally high degree.
The inductive principle has less self-evidence
than some of the other principles of logic,
such as " what follows from a true premiss
must be true." Memories have a diminish-
ing self-evidence as they become remoter and
fainter ; the truths of logic and mathematics
have (broadly speaking) less self-evidence as
they become more complicated. Judgments
of intrinsic ethical or aesthetic value are apt
to have some self-evidence, but not much.

Degrees of self-evidence are important in
the theory of knowledge, since, if proposi-
tions may (as seems likely) have some degree
of self-evidence without being true, it will
not be necessary to abandon all connection
between self-evidence and truth, but merely
to say that, where there is a conflict, the
more self-evident proposition is to be retained
and the less self-evident rejected.

It seems, however, highly probable that
two different notions are combined in " self-
evidence " as above explained ; that one of
them, which corresponds to the highest

ON INTUITIVE KNOWLEDGE 185

degree of self-evidence, is really an infallible
guarantee of truth, while th^ other, which
corresponds to all the other degrees, does
not give an infallible guarantee, but only a
greater or less presumption. This, however,
is only a suggestion, which we cannot as yet
develop further. After we have dealt with
the nature of truth, we shall return to the
subject of self -evidence, in connection with
the distinction between knowledge and error.

CHAPTER XII

TRUTH AND FALSEHOOD

Our knowledge of truths, unlike our
knowledge of things, has an opposite, namely
error. So far as things are concerned, we may
know them or not know them, ^ut there is no
positive state of mind which can be described
as erroneous knowledge of things, so long, at
any rate, as we confine ourselves to knowledge
by acquaintance. Whatever we are ac-
quainted with must be something : we may
draw wrong inferences from our acquaintance,
but the acquaintance itself cannot be decep-
tive. Thus there is no dualism as regards
acquaintance. But as regards knowledge of
truths, there is a dualism. We may believe
what is false as well as what is true. We
know that on very many subjects differ-
ent people hold different and incompatible
186

TRUTH AND FALSEHOOD 187

opinions : hence some Reliefs must be erro-
neous. Since erroneous beliefs are often held
just as strongly as true beliefs, it becomes
a difficult question how they are to be dis-
tinguished from true beliefs. How are we to
know, in a given case, that our belief is not
erroneous ? This is a question of the very
greatest difficulty, to which no completely
sajisf act orx answer _ij_.^^ There is,

however, a preliminary question which is
rather less difficult, and that is : What do we
mean by trilth and falsehood ? It is this
preliminary question which is to be considered
in this chapter.

In this chapter we are not asking how we
can know whether a belief is true or false : we
are asking what is meant by the question
whether a belief is true or false. It is to be
hoped that a clear answer to this question
may help us to obtain an answer to the ques-
tion what beliefs are true, but for the present
we ask only " Vfhat is truth ? " and " What
is falsehood ? " not " What beliefs are true ? "
and " What beliefs are false ? " It is very
important to keep these different questions

r^

188 THE PROBLEMS OF PHILOSOPHY

entirely separate, since any confusion between
them is sure to produce an answer which is
not really applicable to either.

There are three points to observe in the
attempt to discover the nature of truth, three
requisites which any theory must fulfil.

(1) Our theory of truth must be such as to
admit of its opposite, falsehood. A good
many philosophers have failed adequately to
satisfy this condition : they have constructed
theories according to which all our thinking
ought to have been true, and have then had
the greatest difficulty in finding a place for
falsehood. In this respect our theory of
belief must differ from our theory of acquaint-
ance, since in the case of acquaintance it
was not necessary to take account of any
opposite.

(2) It seems fairly evident that if there
were no beliefs there could be no falsehood,
and no truth either, in the sense in which
truth is correlative to falsehood. If we
imagine a world of mere matter, there would
be no room for falsehood in such a world,
and although it would contain what may be

I

TRUTI AND FALSEHOOD 189

called " facts," it would not contain any
truths, in the sense in which truths are things
of the same kind as falsehoods. In fact,
truth and falsehood are properties of beliefs
and statements: hence a world of mere
matter, since it would contain no beliefs or
statements, would also contain no truth or
falsehood.

(3) But, as against what we have just said,
it is to be observed that the truth or falsehood
of a belief always depends upon something
which lies outside the belief itself. If I be-
lieve that Charles I. died on the scaffold, I
believe truly, not because of any intrinsic
quality of my belief, which could be dis-
covered by merely examining the belief, but
because of an historical event which happened
two and a half centuries ago. If I believe
that Charles I. died in his bed, I believe
falsely : no degree of vividness in my belief,
or of care in arriving at it, prevents it from
being false, again because of what happened
long ago, and not because of any intrinsic
property of my belief. Hence, although truth j
and falsehood are properties of beliefs, they

190 THE PROBLEMS OF PHILOSOPHY

are properties dependent upon the relations
of the behefs to other things, not upon any
internal quality of the beliefs.

The third of the above requisites leads us to
adopt the view — which has on the whole
been commonest among philosophers — ^that
truth consists in some form of correspondence
between belief and fact. It is, however, by
no means an easy matter to discover a form
of correspondence to which there are no
irrefutable objections. By this partly — and
partly by the feeling that, if truth consists
in a correspondence of thought with some-
thing outside thought, thought can never
know when truth has been attained — many
philosophers have been led to try to find some
definition of truth which shall not consist in
relation to something wholly outside belief.
The most important attempt at a definition
of this sort is the theory that truth consists
in coherence. It is said that the mark of
falsehood is failure to cohere in the body of
our beliefs, and that it is the essence of a
truth to form part of the completely rounded
system which is The Truth.

TRUTH AND FALSEHOOD 191

There is, however, a great difficulty in this
view, or rather two great difficulties. The
first is that there is no reason to suppose that
only one coherent body of beliefs is possiHle.
It may be that, with sufficient imagination, a
novelist might invent a past for the world
that would perfectly fit on to what we know,
and yet be quite different from the real past.
In more scientific matters, it is certain that
there are often two or more hypotheses which
account for all the known facts on some sub-
ject, and although, in such cases, men of
science endeavour to find facts which will
rule out all the hypotheses except one, there
is no reason why they should always succeed.

In philosophy, again, it seems not un-
common for two rival hypotheses to be both
able to account for all the facts. Thus, for
example, it is possible that life is one long
dream, and that the outer world has only that
degree of reality that the objects of dreams
have ; but although such a view does not
seem inconsistent with known facts, there is
no reason to prefer it to the common-sense
view, according to which other people and

192 THE PROBLEMS OF PHILOSOPHY

things do really exist. Thus coherence as
the definition of truth fails because there is
no proof that there can be only one coherent
system.

The other objection to this definition of
truth is that it assumes the meaning of '' co-
herence " known, whereas, in fact, " coher-
ence " presupposes the truth of the laws of
logic. Two propositions are coherent when
both may be true, and are incoherent when
one at least must be false. Now in order to
know whether two propositions can both be
true, we must know such truths as the law
of contradiction. For example, the two
propositions " this tree is a beech " and
" this tree is not a beech," are not coherent,
because of the law of contradiction. But
if the law of contradiction itself were sub-
jected to the test of coherence, we should find
that, if we choose to suppose it false, nothing
will any longer be incoherent with anything
else. Thus the laws of logic supply the
skeleton or framework within which the test
of coherence applies, and they themselves
cannot be established by this test.

TRUTH AND FALSEHOOD 193

For the above two reasons, coherence
cannot be accepted as giving the meaning of
truth, though it is often a most important
test of truth after a certain amount of truth
has become known.

Hence we are driven back to correspondence
with fact as constituting the nature of truth.
It remains to define precisely what we mean , ,
by " fact,'* and what is the nature of the
correspondence which must subsist between
behef and fact, in order that behef may be
true.

In accordance with our three requisites,
we have to seek a theory of truth which
(1) allows truth to have an opposite, namely
falsehood, (2) makes truth a property of
beliefs, but (3) makes it a property wholly
dependent upon the relation of the beliefs
to outside things.

The necessity of allowing for falsehood
makes it impossible to regard belief as a
relation of the mind to a single object, which
could be said to be what is believed. If
belief were so regarded, we should find that,
like acquaintance, it would not admit of the
a

194 THE PROBLEMS OF PHILOSOPHY

opposition of truth and falsehood, but would
have to be always true. This may be made
clear by examples. Othello believes falsely
that Desdemona loves Cassio. We cannot
say that this belief consists in a relation to a
single object, " Desdemona's love for Cassio,"
for if there were such an object, the belief
would be true. There is in fact no such
object, and therefore Othello cannot have
any relation to such an object. Hence his
belief cannot possibly consist in a relation to
this object.

It might be said that his belief is a relation
to a different object, namely " that Desde-
mona loves Cassio " ; but it is almost as
difficult to suppose that there is such an
object as this, when Desdemona does not love
Cassio, as it was to suppose that there is
" Desdemona's love for Cassio." Hence it
will be better to seek for a theory of belief
which does not make it consist in a relation
of the mind to a single object.

It is common to think of relations as though
they always held between two terms, but in
fact this is not always the case. Some re-

TRUTH AND FALSEHOOD 195

lations demand three terms, some four, and
so on. Take, for instance, the relation
" between." So long as only two terms
come in, the relation " between " is im-
possible : three terms are the smallest number
that render it possible. York is between
London and Edinburgh ; but if London and
Edinburgh were the only places in the world,
there could be nothing which was between
one place and another. Similarly jealousy
requires three people : there can be no sucn
relation that does not involve three at least.
Such a proposition as " A wishes B to promote
C's marriage with D " involves a relation of
four terms ; that is to say, A and B and C and
D all come in, and the relation involved canjiot
be expressed otherwise than in a form in-
volving all four. Instances might be multi-
plied indefinitely, but enough has been said
to show that there are relations which re-
quire more than two terms before they can
occur.

The relation involved in judging or he-
lieving must, if falsehood is to be duly allowed
for, be taken to be a relation between several

196 THE PROBLEMS OF PHILOSOPHY

terms, not between two. When Othello
believes that Desdemona loves Cassio, he
must not have before his mind a single object,
" Desdemona's love for Cassio," or " that
Desdemona loves Cassio," for that would
require that there should be objective false-
hoods, which subsist independently of any
minds ; and this, though not logically re-
futable, is a theory to be avoided if possible.
Thus it is easier to account for falsehood if
we take judgment to be a relation in which
the mind and the various objects concerned
all occur severally ; that is to say, Desdemona
and loving and Cassio must all be terms in
the relation which subsists when Othello
believes that Desdemona loves Cassio. This
relation, therefore, is a relation of four terms,
since Othello also is one of the terms of the
relation. When we say that it is a relation of
four terms, we do not mean that Othello has
a certain relation to Desdemona, and has the
same relation to loving and also to Cassio.
This may be true of some other relation than
believing; but believing, plainly, is not a
relation which Othello has to each of the three

TRUTH AND FALSEHOOD 197

terms concerned, but to all of them together :
there is only one example of the relation of
believing involved, but this one example
knits together four terms. Thus the actual
occurrence, at the moment when Othello is
entertaining his belief, is that the relation
called "believing" is knitting together into
one complex whole the four terms Othello,
Desdemona, loving, and Cassio. What is
called belief or judgment is nothing but this
relation of believing or judging, which relates
a mind to several things other than itself. An
act of belief or of judgment is the occurrence
between certain terms at some particular
time, of the relation of believing or judging.
We are now in a position to understand
what it is that distinguishes a true judgment
from a false one. For this purpose we will
adopt certain definitions. In every act of
judgment there is a mind which judges, and
there are terms concerning which it judges.
We will call the mind the subject in the
judgment, and the remaining terms the
objects. Thus, when Othello judges that Des-
demona loves Cassio, Othello is the subject,

198 THE PROBLEMS OF PHILOSOPHY

while the objects are Desdemona and loving
and Cassio. The subject and the objects
together are called the constituents of the
judgment. It will be observed that the
relation of judging has what is called a
" sense " or " direction." We may say, meta-
phorically, that it puts its objects in a certain
order, which we may indicate by means of
the order of the words in the sentence. (In
an inflected language, the same thing will
be indicated by inflections, e.g. by the differ-
ence between nominative and accusative.)
Othello's judgment that Cassio loves Desde-
mona differs from his judgment that Desde-
mona loves Cassio, in spite of the fact that it
consists of the same constituents, because the
relation of judging places the constituents
in a different order in the two cases. Simi-
larly, if Cassio judges that Desdemona loves
Othello, the constituents of the judgment are
still the same, but their order is different.
This property of having a " sense "or "di-
rection " is one which the relation of judging
shares with all other relations. The " sense "
of relations is the ultimate source of order

TRUTH AND FALSEHOOD 199

and series and a host of mathematical con-
cepts ; but we need not concern ourselves
further with this aspect.

We spoke of the relation called " judging "
or " believing " as knitting together into one
complex whole the subject and the objects.
In this respect, judging is exactly like every
other relation. Whenever a relation holds
between two or more terms, it unites the
terms into a complex whole. If Othello
loves Desdemona, there is such a complex
whole as " Othello's love for Desdemona."
The terms united by the relation may be
themselves complex, or may be simple, but
the whole which results from their being
united must be complex. Wherever there
is a relation which relates certain terms, there
is a complex object formed of the union
of those terms; and conversely, wherever
there is a complex object, there is a relation
which relates its constituents. When an
act of believing occurs, there is a complex,
in which *' believing " is the uniting re-
lation, and subject and objects are arranged
in a certain order by the " sense " of the

200 THE PROBLEMS OF PHILOSOPHY

relation of believing. Among the objects,
as we saw in considering " Othello believes
that Desdemona loves Cassio," one must be
a relation — in this instance, the relation
" loving." But this relation, as it occurs in
the act of beheving, is not the relation which
creates the unity of the complex whole con-
sisting of the subject and the objects. The
relation " loving," as it occurs in the act of
believing, is one of the objects — it is a brick
in the structure, not the cement. The
cement is the relation " believing." When
the belief is true^ there js anjotherjjom^lex
unity, in which the relation which was one
cnEEe objects^ofjh^e bejieiLrelates the other
objects. Thus, e.g., if Othello believes truly
that Desdemona loves Cassio, then there is
a complex unity, " Desdemona's love for
Cassio," which is composed exclusively of
the objects of the belief, in the same order as
they had in the belief, with the relation which
was one of the objects occurring now as the
cement that binds together the other objects
of the belief. On the other hand, when a
belief is falset there is no such complex unity

TRUTH AND FALSEHOOD 201

composed only of the objects of the oeHef.
If Othello believes falsely that Desdemona
loves Cassio, then there is no such complex
unity as " Desdemona's love for Cassio."

Thus a belief is true when it corresponds to
a\;ertain associated complex, and false when
it does not. Assuming, for the sake of defi-
niteness, that the objects of the belief are
two terms and a relation, the terms being put
in a certain order by the *' sense " of the
believing, then if the two terms in that order
are united by the relation into a complex,
the belief is true ; if not, it is false. This
constitutes the definition of truth and false-
hood that we were in search of. Judging or
believing is a certain complex unity of which
a mind is a constituent ; if the remaining
constituents, taken in the order which they
have in the belief, form a complex unity,
then the belief is true ; if not, it is false.

Thus although truth and falsehood are
properties of beliefs, yet they are in a sense
extrinsic properties, for the condition of the
truth of a belief is something not involving
beliefs, or (in general) any mind at all, but

202 THE PROBLEMS OF PHILOSOPHY

only the objects of the belief. A mind, which
believes, believes truly when there is a corre-
sponding complex not involving the mind, but
only its objects. This correspondence ensures
truth, and its absence entails falsehood.
Hence we account simultaneously for the two
facts that beliefs (a) depend on minds for
their existence, {b) do not depend on minds
for their truth.

We may restate our theory as follows : If
we take such a belief as " Othello believes
that Desdemona loves Cassio," we will call
Desdemona and Cassio the object-terms, and
loving the object-relation. If there is a com-
plex unity " Desdemona's love for Cassio,'*
consisting of the object-terms related by the
object-relation in the same order as they have
in the belief, then this complex unity is called
the fact corresponding to the belief. Thus a
belief is true when there is a corresponding
fact, and is false when there is no correspond-
ing fact.

It will be seen that minds do not create
truth or falsehood. They create beliefs, but
when once the beliefs are created, the mind

TRUTH AND FALSEHOOD 203

cannot make them true or false, except in the
special case where they concern future things
which are within the power of the person
believing, such as catching trains. What
makes a belief true is a fact, and this fact does
not (except in exceptional cases) in any way
involve the mind of the person who has the
belief.

Having now decided what we mean by
truth and falsehood, we have next to consider
what ways there are of knowing whether this
or that belief is true or false. This considera-
tion will occupy the next chapter.

CHAPTER XIII

KNOWLEDGE, ERROR, AND PROBABLE
OPINION

The question as to what we mean by truth
and falsehood, which we considered in the
preceding chapter, is of much less interest
than the question as to how we can know what
is true and what is false. This question will
occupy us in the present chapter. There can
be no doubt that some of our beliefs are
erroneous ; thus we are led to inquire what
certainty we can ever have that such and
such a belief is not erroneous. In other words,
can we ever hnow anything at all, or do we
merely sometimes by good luck believe what
is true ? Before we can attack this question,
we must, however, first decide what we mean
by " knowing," and this question is not so
easy as might be supposed.

204

KNOWLEDGE AND ERROR 205'

At first sight we might imagine that know-
ledge could be defined as " true belief.''
When what we believe is true, it might be
supposed that we had achieved a knowledge
of what we believe. But this would not ac-
cord with the way in which the word is
commonly used. To take a very trivial in-
stance : If a man believes that the late
Prime Minister's last name began with a B, he
believes what is true, since the late Prime
Minister was Sir Henry Campbell Bannerman.
But if he believes that Mr. Balfour was the
late Prime Minister, he will still believe that
the late Prime Minister's last name began
with a B, yet this belief, though true, would
not be thought to constitute knowledge. If a
newspaper, by an intelligent anticipation,
announces the result of a battle before any
telegram giving the result has been received, it
may by good fortune announce what after-
wards turns out to be the right result, and it
may produce belief in some of its less experi-
enced readers. But in spite of the truth of
their belief, they cannot be said to have know-
ledge. Thus it is clear that a true belief is not

206 THE PROBLEMS OF PHILOSOPHY

knowledge when it is deduced from a false
belief.

In like manner, a true belief cannot be
called knowledge when it is deduced by a
fallacious process of reasoning, even if the
premisses from which it is deduced are true.
If I know that all Greeks are men and that
Socrates was a man, and I infer that Socrates
was a Greek, I cannot be said to know that
Socrates was a Greek, because, although my
premisses and my conclusion are true, the
conclusion does not follow from the premisses.

But are we to say that nothing is knowledge
except what is validly deduced from true
premisses ? Obviously we cannot say this.
Such a definition is at once too wide and too
narrow. In the first place, it is too wide,
because it is not enough that our premisses
should be true, they must also be known. The
man who believes that Mr. Balfour was the
late Prime Minister may proceed to draw
valid deductions from the true premiss that the
late Prime Minister's name began with a B,
but he cannot be said to know the conclusions
reached by these deductions. Thus we shall

KNOWLEDGE AND ERROR 207

have to amend our definition by saying that
knowledge is what is validly deduced from
known premisses. This, however, is a cir-
cular definition : it assumes that we already
know what is meant by " known premisses."
It can, therefore, at best define one sort of
knowledge, the sort we call derivative, as
opposed to intuitive knowledge. We may
say : " Derivative knowledge is what is validly
deduced from premisses known intuitively.'* /(
In this statement there is no formal defect,
but it leaves the definition of intuitive know-
ledge still to seek.

Leaving on one side, for the moment, the
question of intuitive knowledge, let us con-
sider the above suggested definition of de-
rivative knowledge. The chief objection to
it is that it unduly limits knowledge. It
constantly happens that people entertain a
true belief, which has grown up in them be-
cause of some piece of intuitive knowledge from
which it is capable of being validly inferred,
but from which it has not, as a matter of fact,
been inferred by any logical process.

Take, for example, the beliefs produced by

208 THE PROBLEMS OF PHILOSOPHY

reading. If the newspapers announce the
death of the King, we are fairly well justified
in believing that the King is dead, since this
is the sort of announcement which would not
be made if it were false. And we are quite
amply justified in believing that the news-
paper asserts that the King is dead. But here
the intuitive knowledge upon which our belief
is based is knowledge of the existence of sense-
data derived from looking at the print which
gives the news. This knowledge scarcely
rises into consciousness, except in a person
who cannot read easily. A child may be
aware of the shapes of the letters, and pass
gradually and painfully to a realisation of
their meaning. But anybody accustomed to
reading passes at once to what the letters
mean, and is not aware, except on reflection,
that he has derived this knowledge from the
sense-data called seeing the printed letters.
Thus although a valid inference from the
letters to their meaning is possible, and could
be performed by the reader, it is not in fact
performed, since he does not in fact perform
any operation which can be called logical

KNOWLEDGE AND ERROR 209

inference. Yet it would be absurd to say
that the reader does not know that the news-
paper announces the King's death.

We must, therefore, admit as derivative
knowledge whatever is the result of intuitive ^'
knowledge even if by mere association, pro-
vided there is a valid logical connection, and
the person in question could become aware of
this connection by reflection. There are in
fact many ways, besides logical inference, by
which we pass from one belief to another : the
passage from the print to its meaning illus-
trates these ways. These ways may be called
"psychological inference." We shall, then,
admit such psychological inference as a means
of obtaining derivative knowledge, provided
there is a discoverable logical inference which
runs parallel to the psychological inference.
This renders our definition of derivative know-
ledge less precise than we could wish, since
the word " discoverable " is vague : it does
not tell us how much reflection may be needed
in order to make the discovery. But in fact
" knowledge " is not a precise conception : it j
merges into " probable opinion," as we shall ^

210 THE PROBLEMS OF PHILOSOPHY

see more fully in the course of the present
chapter. A very precise definition, therefore,
should not be sought, since any such definition
must be more or less misleading.

The chief difficulty in regard to knowledge,
however, does not arise over derivative know-
ledge, but over intuitive knowledge. So long
as we are dealing with derivative knowledge,
we have the test of intuitive knowledge to fall
back upon. But in regard to intuitive beliefs,
it is by no means easy to discover any criterion
by which to distinguish some as true and
others as erroneous. In this question it is
scarcely possible to reach any very precise
^ result : all our knowledge of truths is infected
with some degree of doubt, and a theory which
ignored this fact would be plainly wTong.
Something may be done, however, to mitigate
the difficulties of the question.

Our theory of truth, to begin with, supplies
the possibility of distinguishing certain truths
as self-evident in a sense which ensures in-
fallibility. When a belief is true, we said,
there is a corresponding fact, in which the
several objects of the belief form a single

. KNOWLEDGE AND ERROR 211

complex. The belief is said to constitute
knowledge of this fact, provided it fulfils those
further somewhat vague conditions which we
have been considering in the present chapter.
But in regard to any fact, besides the know-
ledge constituted by belief, we may also have
the kind of knowledge constituted by yet-
ception (taking this word in its widest possible
sense). For example, if you know the hour
of the sunset, you can at that hour know the
fact that the sun is setting : this is knowledge
of the fact by way of knowledge of truths ;
but you can also, if the weather is fine, look
to the west and actually see the setting sun :
you then know the same fact by the way of
knowledge of things.

Thus in regard to any complex fact, there
are, theoretically, two ways in which it may
be known : (1) by means of a judgment, in
which its several parts are judged to be
related as they are in fact related ; (2) by
means of acquaintance with the complex fact
itself, which may (in a large sense) be called
perception, though it is by no means confined
to objects of the senses. Now it will be

212 THE PROBLEMS OF PHILOSOPHY

observed that the second way of knowing a
complex fact, the way of acquaintance, is
!rV>*fc, only possible when there really is such a fact,
while the first way, like all judgment, is
liable to error. The second way gives us
the complex whole, and is therefore only
possible when its parts do actually have that
relation which makes them combine to form
such a complex. The first way, on the con-
trary, gives us the parts and the relation
severally, and demands only the reality of
the parts and the relation : the relation may
not relate those parts in that way, and yet
the judgment may occur.

It will be remembered that at the end of
Chapter XI we suggested that there might
be two kinds of self-evidence, one giving an
absolute guarantee of truth, the other only a
partial guarantee. These two kinds can now
be distinguished.

We may say that a truth is self-evident,

. in the first and most absolute sense, when

we have acquaintance with the fact which

corresponds to the truth. When Othello

believes that Desdemona loves Cassio, the

KNOWLEDGE AND ERROR 213

corresponding fact, if his belief were true,
would be " Desdemona's love for Cassio."
This would be a fact with which no one could
have acquaintance except Desdemona ; hence
in the sense of self -evidence that we are con-
sidering, the truth that Desdemona loves
Cassio (if it were a truth) could only be self-
evident to Desdemona. All mental facts,
and all facts concerning sense-data, have this ^
same privacy : there is only one person to ?
whom they can be self-evident in our present
sense, since there is only one person who can
be acquainted with the mental things or the
sense-data concerned. Thus no fact about
any particular existing thing can be self-
evident to more than one person. On the
other hand, facts about universals do not
have this privacy. Many minds may be ^^
acquainted with the same universals ; hence
a relation between universals may be known
by acquaintance to many different people.
In all cases where we know by acquaintance
a complex fact consisting of certain terms in
a certain relation, we say that the truth that
these terms are so related has the first or

214 THE PROBLEMS OF PHILOSOPHY

absolute kind of self-evidence, and in these
cases the judgment that the terms are so
related must be true. Thus this sort of self-
evidence is an absolute guarantee of truth.

But although this sort of self-evidence is an
absolute guarantee of truth, it does not enable
us to be absolutely certain, in the case of any-
given judgment, that the judgment in ques-
tion is true. Suppose we first perceive the
sun shining, which is a complex fact, and
thence proceed to make the judgment " the
sun is shining." In passing from the per-
ception to the judgment, it is necessary to
analyse the given complex fact : we have to
separate out " the sun " and " shining " as
constituents of the fact. In this process it
is possible to commit an error ; hence even
where a jact has the first or absolute kind of
self -evidence, a judgment believed to corre-
spond to the fact is not absolutely infallible,
because it may not really correspond to the
fact. But if it does correspond (in the sense
explained in the preceding chapter), then it
must be true.

The second sort of self -evidence will be that

KNOWLEDGE AND ERROR 215

which belongs to judgments in the first
instance, and is not derived from direct
perception of a fact as a single complex
whole. This second kind of self-evidence
will have degrees, from the very highest
degree down to a bare inclination in favour
of the belief. Take, for example, the case of
a horse trotting away from us along a hard
road. At first our certainty that we hear the
hoofs is complete ; gradually, if we listen
intently, there comes a moment when we
think perhaps it was imagination or the blind
upstairs or our own heart-beats ; at last we
become doubtful whether there was any noise
at all ; then we think we no longer hear
anything, and at last we know we no longer
hear anything. In this process, there is a
continual gradation of self -evidence, from the
highest degree to the least, not in the sense-
data themselves, but in the judgments based
on them.

Or again: Suppose we are comparing two
shades of colour, one blue and one green.
We can be quite sure they are different shades
of colour ; but if the green colour is gradually

210 THE PROBLEMS OF PHILOSOPHY

altered to be more and more like the blue,
becoming first a blue -green, then a greeny-
blue, then blue, there will come a moment
when we are doubtful whether we can see any
difference, and then a moment when we
know that we cannot see any difference.
The same thing happens in tuning a musical
instrument, or in any other case where there
is a continuous gradation. Thus self -evidence
of this sort is a matter of degree ; and it
seems plain that the higher degrees are more
to be trusted than the lower degrees.

In derivative knowledge our ultimate
premisses must have some degree of self-
evidence, and so must their connection with
the conclusions deduced from them. Take for
jexample a piece of reasoning in geoitietry.
It is not enough that the axioms from which
we start should be self-evident : it is necessary
also that, at each step in the reasoning, the
connection of premiss and conclusion should
be self-evident. In difficult reasoning, this
connection has often only a very small degree
of self -evidence ; hence errors of reasoning are
not improbable where the difficulty is great.

KNOWLEDGE AND ERROR 217

From what has been said it is evident that,
both as regards intuitive knowledge and as
regards derivative knowledge, if we assume
that intuitive knowledge is trustworthy in
proportion to the degree of its self -evidence,
there will be a gradation in trustworthiness,
from the existence of noteworthy sense-data
and the simpler truths of logic and arith-
metic, which may be taken as quite certain,
down to judgments which seem only just
more probable than their opposites. What
we firmly believe, if it is true, is called know- *^ '
ledgCy provided it is either intuitive or in-
ferred (logically or psychologically) from\.,,.
intuitive knowledge from which it follows '>^*
logically. What we firmly believe, if it is not *^^ '^
true, is called error. What we firmly believe,**
if it is neither knowledge nor error, and also
what we believe hesitatingly, because it is,
or is derived from, something which has not
the highest degree of self-evidence, may be
called probable opinion. Thus the greater
part of what would commonly pass as know-
ledge is more or less probable opinion^

In regard to probable opinion, we can v^

218 THE PROBLEMS OF PHILOSOPHY

derive great assistance from coherence, which
we rejected as the definition of truth, but may
often use as a criterion. A body of individu-
ally probable opinions, if they are mutually
coherent, become more probable than any one
of them would be individually. It is in this
way that many scientific hypotheses acquire
their probability. They fit into a coherent
system of probable opinions, and thus become
more probable than they would be in isola-
tion. The same thing applies to general
philosophical hypotheses. Often in a single
case such hypotheses may seem highly doubt-
ful, while yet, when we consider the order
and coherence which they introduce into a
mass of probable opinion, they become pretty
nearly certain. This applies, in particular,
to such matters as the distinction between
dreams and waking life. If our dreams, night
after night, were as coherent one with another
as our days, we should hardly know whether
to believe the dreams or the waking life.
As it is, the test of coherence condemns the
dreams and confirms the waking life. But
this test, though it increases probability

KNOWLEDGE AND ERROR 219

wnere it is successful, never gives absolute
certainty, unless there is certainty already
at some point in the coherent system. Thus
the mere organisation of probable opinion
will never, by itself, transform it into in-
dubitable knowledge.

CHAPTER XIV

THE LIMITS OF PHILOSOPHICAL KNOW-
LEDGE

In all that we have said hitherto concerning
philosophy, we have scarcely touched on many
matters that occupy a great space in the
writings of most philosophers. Most philo-
sophers— or, at any rate, very many — ^profess
to be able to prove, by a 'priori metaphysical
reasoning, such things as the fundamental
dogmas of religion, the essential rationality
of the universe, the illusoriness of matter, the
unreality of all evil, and so on. There can be
no doubt that the hope of finding reason to
believe such theses as these has been the
chief inspiration of many life-long students
of philosophy. This hope, I believe, is vain.
It would seem that knowledge concerning the
universe as a whole is not to be obtained by

THE LIMITS OF KNOWLEDGE 221

metaphysics, and that the proposed proofs
that, in virtue of the laws of logic, such and
such things must exist and such and such
others cannot, are not capable of surviving a
critical scrutiny. In this chapter we shall
briefly consider the kind of way in which
such reasoning is attempted, with a view
to discovering whether we can hope that it
may be valid.

The great representative, in modern times,
of the kind of view which we wish to examine,
was Hegel (1770-1831). Hegel's philosophy
is very difficult, and it is impossible here to do
anything like justice to it. But we may,
without going into details, obtain some con-
ception of the nature of his methods and his
results. /His main thesis is that everything
short of the Whole is obviously fragmentary,
and obviously incapable of existing without
the complement supplied by the rest of the
world. / Just as a comparative anatomist, from
a single bone, sees what kind of animal the
whole must have been, so the metaphysician,
according to Hegel, sees, from any one piece
of reality, what the whole of reality must be —

222 THE PROBLEMS OF PHILOSOPHY

at least in its large outlines. Every ap-
parently separate piece of reality has, as it
were, hooks which grapple it to the next piece ;
the next piece, in turn, has fresh hooks, and so
on, until the whole universe is reconstructed.
This essential incompleteness appears, accord-
ing to Hegel, equally in the world of thought
and in the world of things. In the world of
thought, if we take any idea which is abstract
or incomplete, we find, on examination, that,
if we forget its incompleteness, we become
involved in contradictions ; these contra-
dictions turn the idea in question into its
opposite, or antithesis ; and in order to escape,
we have to find a new, less incomplete idea,
which is the synthesis of our original idea and
its antithesis.

This new idea, though less incomplete than
the idea we started with, will be found, never-
theless, to be still not wholly complete, but to
pass into its antithesis, with which it must be
combined in a new synthesis. In this way
Hegel advances until he reaches thel" Absolute
Idea," which, according to him, has no in-
completeness, no opposite, and no need of

I

THE LIMITS OF KNOWLEDGE 223

further development/ The Absolute Idea,
therefore, is adequate to describe Absolute
Reality ; but all lower ideas only describe
reality as it appears to a partial view, not as
it is to one who simultaneously surveys the
Whole. Thus Hegel reaches the conclusion
that Absolute Reality forms one single har-
monious system, not in space or time, not in
any degree evil, wholly rational, and wholly
spiritual. Any appearance to the contrary, in
the world we know, can be proved logically —
so he believes — to be entirely due to our
fragmentary piecemeal view of the universe.
If we saw the universe whole, as we may
suppose God sees it, space and time and matter
and evil and all striving and struggling would
disappear, and we should see instead an eternal
perfect unchanging spiritual unity.

In this conception, there is undeniably some-
thing sublime : something to which we could
wish to yield assent. Nevertheless, when the
arguments in support of it are carefully
examined, they appear to involve much con-
fusion and many unwarrantable assumptions.
The fundamental tenet upon which the system

i

224 THE PROBLEMS OF PHILOSOPHY

is built up is that what is incomplete must be
not self-subsistent, but must need the support
of other things before it can exist, jlt is held
that whatever has relations to things outside
itself must contain some reference to those
outside things in its own nature, and could
not, therefore, be what it is if those outside
things did not exist.\ A man's nature, for
example, is constituted by his memories and
the rest of his knowledge, by his loves and
hatreds, and so on ; thus, but for the objects
which he knows or loves or hates, he could
not be what he is. He is essentially and
obviously a fragment : taken as the sum-total
of reality he would be self-contradictory.

This whole point of view, however, turns
upon the notion of the " nature " of a thing,
which seems to mean '' all the truths about
the thing." It is of course the case that a
truth which connects one thing with another
thing could not subsist if the other thing
did not subsist. But a truth about a thing
is not part of the thing itself, although it
must, according to the above usage, be part
of the " nature " of the thing. If we mean

I

THE LIMITS OF KNOWLEDGE 225

by a thing's " nature " all the truths about the
thing, then plainly we cannot know a thing's
" nature " unless we know all the thing's re-
lations to all the other things in the universe.
But if the word " nature " is used in this
sense, we shall have to hold that the thing
may be known when its " nature " is not
known, or at any rate is not known completely.
There is a confusion, when this use of the
word " nature " is employed, between know-
ledge of things and knowledge of truths. We
may have knowledge of a thing by acquaint-
ance even if we know very few propositions
about it — theoretically we need not know any
propositions about it. Thus, acquaintance
with a thing does not involve knowledge of its
*' nature " in the above sense. And although
acquaintance with a thing is involved in our
knowing any one proposition about a thing,
knowledge of its " nature," in the above sense,
is not involved. Hence, (1) acquaintance with
a thing does not logically involve a knowledge
of its relations, and (2) a knowledge of some of
its relations does not involve a knowledge
of all of its relations nor a knowledge of its

226 THE PROBLEMS OF PHILOSOPHY

*' nature " in the above sense. I may be ac-
quainted, for example, with my toothache,
and this knowledge may be as complete as
knowledge by acquaintance ever can be, with-
out knowing all that the dentist (who is not
acquainted with it) can tell me about its
cause, and without therefore knowing its
" nature " in the above sense. Thus the fact
that a thing has relations does not prove that
its relations are logically necessary. That is
to say, from the mere fact that it is the thing
it is we cannot deduce that it must have the
various relations which in fact it has. This
only seems to follow because we know it
already.

fit follows that we cannot prove that the
universe as a whole forms a single harmonious
system such as Hegel believes that it forms.
And if we cannot prove this, we also cannot
prove the unreality of space and time and
matter and evil, for this is deduced by Hegel
from the fragmentary and relational character
of these things. Thus we are left to the
piecemeal investigation of the world, and are
unable to know the characters of those parts

THE LIMITS OF KNOWLEDGE 227

of the universe that are remote from our ex-
perience. This result, disappointing as it is
to those whose hopes have been raised by the
systems of philosDphers, is in harmony with
the inductive and scientific temper of our age,
and is borne out by the whole examination
of human knowledge which has occupied our
previous chapters.

Most of the great ambitious attempts of
metaphysicians have proceeded by the at-
tempt to prove that such and such apparent
features of the actual world were self-contra-
dictory, and therefore could not be real. The
whole tendency of modern thought, however,
is more and more in the direction of showing
that the supposed contradictions were illusory,
and that very little can be proved a priori
from considerations of what must be. A good
illustration of this is afforded by space and
time. Space and time appear to be infinite
in extent, and infinitely divisible. If we
travel along a straight line in either direction,
it is difficult to believe that we shall finally
reach a last point, beyond which there is
nothing, not even empty space. Similarly, if

228 THE PROBLEMS OF PHILOSOPHY

in imagination we travel backwards or for-
wards in time, it is difficult to believe that we
shall reach a first or last time, with not even
empty time beyond it. Thus space and time
appear to be infinite in extent.

Again, if we take any two points on a line,
it seems evident that there must be other
points between them, however small the dis-
tance between them may be : every distance
can be halved, and the halves can be halved
again, and so on ad infinitum. In time,
similarly, however little time may elapse
between two moments, it seems evident that
there will be other moments between them.
Thus space and time appear to be infinitely
divisible. But as against these apparent facts
— infinite extent and infinite divisibility —
philosophers have advanced arguments tend-
ing to show that there could be no infinite
collections of things, and that therefore the
number of points in space, or of instants in
time, must be finite. Thus a contradiction
emerged between the apparent nature of space
and time and the supposed impossibility of
infinite collections.

I

THE LIMITS OF KNOWLEDGE 229

Kant, who first emphasised this contradic-
tion, deduced the impossibiHty of space and
time, which he declared to be merely sub-
jective ; and since his time very many philo-
sophers have believed that space and time
are mere appearance, not characteristic of the
world as it really is. Now, however, owing
to the labours of the mathematicians, notably
Georg Cantor, it has appeared that the impos-
sibility of infinite collections was a mistake.
They are not in fact self-contradictory, but
only contradictory of certain rather obstinate
mental prejudices. Hence the reasons for
regarding space and time as unreal have be-
cosne inoperative, and one of the great sources
of metaphysical constructions is dried up.

The mathematicians, however, have not
been content with showing that space as it is
commonly supposed to be is possible ; they
have shown also that many other forms of
space are equally possible, so far as logic can
show. Some of Euclid's axioms, which appear
to common sense to be necessary, and were
formerly supposed to be necessary by philo-
sophers, are now known to derive their appear-

230 THE PROBLEMS OF PHILOSOPHY

ance of necessity from our mere familiarity
with actual space, and not from any a ^priori
logical foundation. By imagining worlds in
which these axioms are false, the mathemati-
cians have used logic to loosen the prejudices
of common sense, and to show the possibility
of spaces differing — some more, some less —
from that in which we live. And some of these
spaces differ so little from Euclidean space,
where distances such as we can measure are
concerned, that it is impossible to discover by
observation whether our actual space is strictly
Euclidean or of one of these other kinds.
Thus the position is completely reversed.
Formerly it appeared that experience left
only one kind of space to logic, and logic
showed this one kind to be impossible. Now,
logic presents many kinds of space as possible
apart from experience, and experience only
partially decides between them. Thus, while
our knowledge of what is has become less than
it was formerly supposed to be, our knowledge
of what may be is enormously increased. In-
stead of being shut in within narrow walls,
of which every nook and cranny could be

I

THE LIMITS OF KNOWLEDGE 231

explored, we find ourselves in an open
world of free possibilities, where much remains
unknown because there is so much to know.

What has happened in the case of space and
time has happened, to some extent, in other
directions as well. The attempt to prescribe
to the universe by means of a 'priori principles
has broken down ; logic, instead of being, as
formerly, the bar to possibilities, has become
the great liberator of the imagination, present-
ing innumerable alternatives which are closed
to unreflective common sense, and leaving to
experience the task of deciding, where decision
is possible, between the many worlds which
logic offers for our choice. Thus knowledge as
to what exists becomes limited to what we can
learn from experience — not to what we can
actually experience, for, as we have seen, there
is much knowledge by description concerning
things of which we have no direct experience.
But in all cases of knowledge by description,
we need some connection of universals, enab-
ling us, from such and such a datum, to infer
an object of a certain sort as implied by our
datum. Thus in regard to physical objects,

232 THE PROBLEMS OF PHILOSOPHY

for example, the principle that sense-data are
signs of physical objects is itself a connection
of universals ; and it is only in virtue of this
principle that experience enables us to acquire
knowledge concerning physical objects. The
same applies to the law of causality, or, to
descend to what is less general, to such prin-
ciples as the law of gravitation.

Principles such as the law of gravitation
are proved, or rather are rendered highly
probable, by a combination of experience with
some wholly a priori principle, such as the
principle of induction. Thus our intuitive
knowledge, which is the source of all our other
knowledge of truths, is of two sorts : pure
empirical knowledge, which tells us of the
existence and some of the properties of parti-
cular things with which we are acquainted,
and pure a priori knowledge, which gives us
connections between universals, and enables
us to draw inferences from the particular
facts given in empirical knowledge. Our deri-
vative knowledge always depends upon some
pure a priori knowledge and usually also de-
pends upon some pure empirical knowledge.

THE LIMITS OF KNOWLEDGE 233

Philosophical knowledge, if what has been
said above is true, does not differ essentially
from scientific knowledge ; there is no special
source of wisdom which is open to philosophy
but not to science, and the results obtained by
philosophy are not radically different from
those obtained from science. The essential
characteristic of philosophy, which makes it a
study distinct from science, is criticism. It
examines critically the principles employed in
science and in daily life ; it searches out any in-
consistencies there may be in these principles,
and it only accepts them when, as the result of
a critical inquiry, no reason for rejecting them
has appeared. If, as many philosophers have
believed, the principles underlying the sciences
were capable, when disengaged from irrelevant
detail, of giving us knowledge concerning the
universe as a whole, such knowledge would
have the same claim on our belief as scientific
knowledge has ; but our inquiry has not re-
vealed any such knowledge, and therefore, as
regards the special doctrines of the bolder
metaphysicians, has had a mainly negative
result. But as regards what would be com-

234 THE PROBLEMS OF PHILOSOPHY

monly accepted as knowledge, our result is in
the main positive: we have seldom found
reason to reject such knowledge as the result
of our criticism, and we have seen no reason
to suppose man incapable of the kind of
knowledge which he is generally believed
to possess.

When, however, we speak of philosophy as
a criticism of knowledge, it is necessary to im-
pose a certain limitation. If we adopt the
attitude of the complete sceptic, placing our-
selves wholly outside all knowledge, and
asking, from this outside position, to be
compelled to return within the circle of
knowledge, we are demanding what is im-
possible, and our scepticism can never be
refuted. For all refutation must begin with
some piece of knowledge which the dispu-
tants share ; from blank doubt, no argument
can begin. Hence the criticism of knowledge
which philosophy employs must not be of
this destructive kind, if any result is to be
achieved. Against this absolute scepticism,
no logical argument can be advanced. But it
is not difficult to see that scepticism of this

THE LIMITS OF KNOWLEDGE 235

kind is unreasonable. Descartes' "methodi-
cal doubt," with which modern philosophy-
began, is not of this kind, but is rather the
kind of criticism which we are asserting to be
the essence of philosophy. His " methodical
doubt " consisted in doubting whatever
seemed doubtful ; in pausing, with each ap-
parent piece of knowledge, to ask himself
whether, on reflection, he could feel certain
that he really knew it. This is the kind of
criticism which constitutes philosophy. Some
knowledge, such as knowledge of the existence
of our sense-data, appears quite indubitable,
however calmly and thoroughly we reflect
upon it. In regard to such knowledge, philo-
sophical criticism does not require that we
should abstain from belief. But there are
beliefs — such, for example, as the belief that
physical objects exactly resemble our sense-
data — ^which are entertained until we begin
to reflect, but are found to melt away when
subjected to a close inquiry. Such beliefs
philosophy will bid us reject, unless some
new line of argument is found to support
them. But to reject the beliefs which do not

236 THE PROBLEMS OF PHILOSOPHY

appear open to any objections, however
closely we examine them, is not reasonable,
and is not what philosophy advocates.

The criticism aimed at, in a word, is not
that which, without reason, determines to re-
ject, but that which considers each piece of
apparent knowledge on its merits, and retains
whatever still appears to be knowledge when
this consideration is completed. That some
risk of error remains must be admitted, since
human beings are fallible. Philosophy may
claim justly that it diminishes the risk of error,
and that in some cases it renders the risk so
small as to be practically negligible. To do
more than this is not possible in a world where
mistakes must occur ; and more than this no
prudent advocate of philosophy would claim
to have performed.

CHAPTER XV

THE VALUE OF PHILOSOPHY

Having now come to the end of our brief
and very incomplete review of the problems
of philosophy, it will be well to consider, in
conclusion, what is the value of philosophy
and why it ought to be studied. It is the
more necessary to consider this question, in
view of the fact that many men, under the
influence of science or of practical affairs, are
inclined to doubt whether philosophy is any-
thing better than innocent but useless trifling,
hair-splitting distinctions, and controversies on
matters concerning which knowledge is im-
possible.

This view of philosophy appears to result,
partly from a wrong conception of the ends
of life, partly from a wrong conception of
the kind of goods which philosophy strives to

237

238 THE PROBLEMS OF PHILOSOPHY

achieve. Physical science, through the me-
dium of inventions, is useful to innumerable j
people who are wholly ignorant of it ; thusj
the study of physical science is to be recom-|
mended, not only, or primarily, because of the '
effect on the student, but rather because of
the effect on mankind in general. This utility
does not belong to philosophy. If the study
of philosophy has any value at all for others
than students of philosophy, it must be only
indirectly, through its effects upon the lives
of those who study it. It is in these effects,
therefore, if anywhere, that the value of
philosophy must be primarily sought.

But further, if we are not to fail in our en-
deavour to determine the value of philosophy,
we must first free our minds from the pre-
judices of what are wrongly called " practical "
men. The " practical " man, as this word is
often used, is one who recognises only material
needs, who realises that men must have food
for the body, but is oblivious of the necessity
of providing food for the mind. If all men
were well off, if poverty and disease had been
reduced to their lowest possible point, there

THE VALUE OF PHILOSOPHY 239

would still remain much to be done to produce
a valuable society ; and even in the existing
world the goods of the mind are at least as
important as the goods of the body. It is
exclusively among the goods of the mind that
the value of philosophy is to be found ; and
only those who are not indifferent to these
goods can be persuaded that the study of
philosophy is not a waste of time.

Philosophy, like all other studies, aims
primarily at knowledge. The knowledge it
aims at is the kind of knowledge which gives
unity and system to the body of the sciences,
and the kind which results from a critical
e' lamination of the grounds of our convictions,
prejudices, and beliefs. But it cannot be
maintained that philosophy has had any very
great measure of success in its attempts to
provide definite answers to its questions. If
you ask a mathematician, a mineralogist, a
historian, or any other man of learning, what
definite body of truths has been ascertained
by his science, his answer will last as long as
you are willing to listen. But if you put the
same question to a philosopher, he will, if he is

240 THE PROBLEMS OF PHILOSOPHY

candid, have to confess that his study has not
achieved positive results such as have been
achieved by other sciences. It is true that
this is partly accounted for by the fact that,
as soon as definite knowledge concerning any
subject becomes possible, this subject ceases
to be called philosophy, and becomes a sepa-
rate science. The whole study of the heavens,
which now belongs to astronomy, was once
included in philosophy ; Newton's great work
was called " the mathematical principles of
natural philosophy." Similarly, the study of
the human mind, which was, until very lately,
a part of philosophy, has now been separated
from philosophy and has become the science
of psychology. Thus, to a great extent, the
uncertainty of philosophy is more apparent
than real : those questions which are already
capable of definite answers are placed in the
sciences, while those only to which, at present,
no definite answer can be given, remain to
form the residue which is called philosophy.

This is, however, only a part of the truth

'concerning the uncertainty of philosophy.

There are many questions — and among them

I

THE VALUE OF PHILOSOPHY 241

those that are of the profoundest interest
to our spiritual life — which, so far as we
can see, must remain insoluble to the human
intellect unless its powers become of quite a
different order from what they are now. Has
the universe any unity of plan or purpose, or
is it a fortuitous concourse of atoms ? Is
consciousness a permanent part of the uni-
verse, giving hope of indefinite growth in
wisdom, or is it a transitory accident on a
small planet on which life must ultimately
become impossible ? Are good and evil of
importance to the universe or only to man ?
Such questions are asked by philosophy, and
variously answered by various philosophers.
But it would seem that, whether answers be
otherwise discoverable or not, the answers
suggested by philosophy are none of them
demonstrably true. Yet, however slight may
be the hope of discovering an answer, it is
part of the business of philosophy to continue
the consideration of such questions, to make us
aware of their importance, to examine all the
approaches to them, and to keep alive that
speculative interest in the universe which is

242 THE PROBLEMS OF PHILOSOPHY

apt to be killed by confining ourselves to
definitely ascertainable knowledge.

Many philosophers, it is true, have held that
philosophy could establish the truth of certain
answers to such fundamental questions. They
have supposed that what is of most importance
in religious beliefs could be proved by strict
demonstration to be true. In order to judge
of such attempts, it is necessary to take a
survey of human knowledge, and to form an.
opinion as to its methods and its limitations.
On such a subject it would be unwise to
pronounce dogmatically ; but if the investi-
gations of our previous chapters have not led
us astray, we shall be compelled to renounce
the hope of finding philosophical proofs of
religious beliefs. We cannot, therefore, in-
clude as part of the value of philosophy any
definite set of answers to such questions.
Hence, once more, the value of philosophy
must not depend upon any supposed body of
definitely ascertainable knowledge to be ac-
quired by those who study it.

The value of philosophy is, in fact, to be
sought largely in its very uncertainty. The

THE VALUE OF PHILOSOPHY 243

man who has no tincture of philosophy goes
through life imprisoned in the prejudices de-
rived from common sense, from the habitual
beliefs of his age or his nation, and from
convictions which have grown up in his mind
without the co-operation or consent of his
deliberate reason. To such a man the world
tends to become definite, finite, obvious ;
common objects rouse no questions, and un-
familiar possibilities are contemptuously re-
jected. As soon as we begin to philosophise,
on the contrary, we find, as we saw in our
opening chapters, that even the most every-
day things lead to problems to which only
very incomplete answers can be given. Philo-
sophy, though unable to tell us with certainty
what is the true answer to the doubts which
it raises, is able to suggest many possibilities
which enlarge our thoughts and free them
from the tyranny of custom. Thus, while
diminishing our feeling of certainty as to what
things are, it greatly increases our knowledge
as to what they may be ; it removes the some-
what arrogant dogmatism of those who have
never travelled into the region of liberating

244 THE PROBLEMS OF PHILOSOPHY

doubt, and it keeps alive our sense of wonder
by showing familiar things in an unfamiliar
aspect.

Apart from its utility in showing unsus-
pected possibilities, philosophy has a value —
perhaps its chief value — ^through the greatness
of the objects which it contemplates, and the
freedom from narrow and personal aims re-
sulting from this contemplation. The life of
the instinctive man is shut up within the
circle of his private interests : family and
friends may be included, but the outer world
is not regarded except as it may help or hinder
what comes within the circle of instinctive
wishes. In such a life there is something
feverish and confined, in comparison with
which the philosophic life is calm and free.
The private world of instinctive interests is a
small one, set in the midst of a great and power-
ful world which must, sooner or later, lay our
private world in ruins. Unless we can so
enlarge our interests as to include the whole
outer world, we remain like a garrison in a
beleaguered fortress, knowing that the enemy
prevents escape and that ultimate surrender

THE VALUE OF PHILOSOPHY 245

is inevitable. In such a life there is no peace,
but a constant strife between the insistence of
desire and the powerlessness of will. In one
way or another, if our life is to be great and
free, we must escape this prison and this
strife.

One way of escape is by philosophic con-
templation. Philosophic contemplation does
not, in its widest survey, divide the universe
into two hostile camps — friends and foes,
lielpful and hostile, good and bad — it views
the whole impartially. Philosophic con-
templation, when it is unalloyed, does not
aim at proving that the rest of the universe
is akin to man. All acquisition of knowledge
is an enlargement of the Self, but this enlarge-
ment is best attained when it is not directly
sought. It is obtained when the desire for
knowledge is alone operative, by a study
which does not wish in advance that its
objects should have this or that character,
but adapts the Self to the characters which
it finds in its objects. This enlargement of
Self is not obtained when, taking the Self as
it is, we try to show that the world is so similar

246 THE PROBLEMS OF PHILOSOPHY

to this Self that knowledge of it is possible
without any admission of what seems alien.
The desire to prove this is a form of self-asser-
tion, and like all self-assertion, it is an obstacle
to the growth of Self which it desires, and of
which the Self knows that it is capable. Self-
assertion, in philosophic speculation as else-
where, views the world as a means to its own
ends ; thus it makes the world of less account
than Self, and the Self sets bounds to the
greatness of its goods. In contemplation,
on the contrary, we start from the not-Self,
and through its greatness the boundaries of
Self are enlarged ; through the infinity of the
universe the mind which contemplates it
achieves some share in infinity.

For this reason greatness of soul is not
fostered by those philosophies which as-
similate the universe to Man. Knowledge is
a form of union of Self and not-Self ; like
all union, it is impaired by dominion, and
therefore by any attempt to force the uni-
verse into conformity with what we find in
ourselves. There is a widespread philosophi-
cal tendency towards the view which tells

THE VALUE OF PHILOSOPHY 247

us that man is the measure of all things,
that truth is man-made, that space and time
and the world of universals are properties of
the mind, and that, if there be anything not
created by the mind, it is unknowable and of
no account for us. This view, if our previous
discussions were correct, is untrue ; but in
addition to being untrue, it has the effect of
robbing philosophic contemplation of all that
gives it value, since it fetters contemplation to
Self. What it calls knowledge is not a union
with the not-Self, but a set of prejudices,
habits, and desires, making an impenetrable
veil between us and the world beyond. The
man who finds pleasure in such a theory of
Jcnowledge is like the man who never leaves
the domestic circle for fear his word might
not be law.

The true philosophic contemplation, on the
contrary, finds its satisfaction in every en-
largement of the not-Self, in everything that
magnifies the objects contemplated, and
thereby the subject contemplating. Every-
thing, in contemplation, that is personal or
private, everything that depends upon habit,

248 THE PROBLEMS OF PHILOSOPHY

self-interest, or desire, distorts the object, and
hence impairs the union which the intellect
seeks. By thus making a barrier between
subject and object, such personal and private
things become a prison to the intellect. The
free intellect will see as God might see, without
a here and now, without hopes and fears,
without the trammels of customary beliefs
and traditional prejudices, calmly, dispassion-
ately, in the sole and exclusive desire of know-
ledge— knowledge as impersonal, as purely
contemplative, as it is possible for man to
attain. Hence also the free intellect will value
more the abstract and universal knowledge
into which the accidents of private history do
not enter, than the knowledge brought by the
senses, and dependent, as such knowledge
must be, upon an exclusive and personal point
of view and a body whose sense-organs distort
as much as they reveal.

The mind which has become accustomed to
the freedom and impartiality of philosophic
contemplation will preserve something of the
same freedom and impartiality in the world of
action and emotion. It will view its purposes

THE VALUE OF PHILOSOPHY 249

and desires as parts of the whole, with the
absence of insistence that results from seeing
them as infinitesimal fragments in a world of
which all the rest is unaffected by any one
man's deeds. The impartiality which, in con-
templation, is the unalloyed desire for truth, is
the very same quality of mind which, in action,
is justice, and in emotion is that universal
love which can be given to all, and not only to
those who are judged useful or admirable.
Thus contemplation enlarges not only the ob-
jects of our thoughts, but also the objects of our
actions and our affections : it makes us citizens
of the universe, not only of one walled city at
war with all the rest. In this citizenship of
the universe consists man's true freedom, and
his liberation from the thraldom of narr'^w
hopes and fears.

Thus, to sum up our discussion of the value
of philosophy : Philosophy is to be studied,
not for the sake of any definite answers to its
questions, since no definite answers can, as a
rule, be known to be true, but rather for the
sake of the questions themselves ; because
these questions enlarge our conception of what

250 THE PROBLEMS OF PHILOSOPHY

is possible, enrich our intellectual imagination,
and diminish the dogmatic assurance which
closes the mind against speculation ; but above
all because, through the greatness of the
universe which philosophy contemplates, the
mind also is rendered great, and becomes
capable of that union with the universe which
constitutes its highest good.

BIBLIOGRAPHICAL NOTE

AThe student who wishes to acquire an elementary know-
lodge of philosophy will find it both easier and more
profitable to read some of the works of the great philo-
sophers than to attempt to derive an all-round view
from hand-books. The following are specially recom-
mended :

Plato : Republic, especially Books VI and VII. Trans-
lated by Davies and Vaughan. Golden Treasury
Series.
Descartes : Meditations. Translated by Haldane and

Ross. Cambridge University Press, 1911.
Spinoza: Ethics. Translated by Hale White and

Amelia Stirling.
Leibniz : The Monadology. Translated by R. Latta.

Oxford, 1898.
Berkeley : Three Dialogues be tweenHylas and Philonous.
Hume : Enquiry concerning Human Understanding,
Kant : Prolegomena to every Future Metaphysic.

251

/

INDEX

The interrogations indicate places where a view ia
diacuaeed, not asserted.

Absolute idea, 222
Acquaintance, 68, 69, 72 ff.,
170, 211

with Self ? 78 ff.
Act, mental, 65
Analytic, 128
Appearance, 12, 24
-4 23non:, 1 16, 1 18, 125, 127ff.,
161 ff.

mental ? 136
Arithmetic, 130
Association, 97, 101

Being, 156
Belief, 186 f?.

instinctive, 37, 39
Berkeley, 18, 22, 24, 56,

60 ff., 114, 149, 151
Bismarck, 85, 89
Bradley, 148

Cat, 35, 36

Causality, 107, 129

China, Emperor of, 70, 116

Cogito, 28

Coherence, 190-3, 218 .

Colours, 11, 12, 13, 54-6,
215

Contemplation, 244

Contradiction, law of , 113,
129

Correspondence of sense-
data and physical ob-
jects, 35, 38, 49, 62-3,
69, 62

Correspondence of belief and

fact, 190 fl.
Critical Philosophy, 126

Deduction, 123
Descartes, 27, 114, 235
Description, 71, 74, 81 &.,

170
Divisibihty, infinite, 227-8
Doubt, 27, 28, 40, 234
Dreams, 30, 34-5, 172, 191
Duration, 50

Empiricists, 114, 134

Error, 172, 186 ff., 217,
236

Excluded Middle, 113

Existence, 155 :

knowledge of, 93, 116

Experience :

immediate, 9, 23, 27, 61
extended by descriptions,
92, 94, 231

Facts, 214
Falsehood, 187 ff.
definition of, 201

Greneralisation, empirical,

121, 125, 166
Geometry, 120, 130

Hallucinations, 30, 172

Hegel, 221 ff.

Hume, 114, 129, 149, 151

253

254

INDEX

Ideas, 61 ff., 155

abstract, 76, 149

innate, 114

Platonic, 142 ff.
Idealism, 58-71

defined, 58

grounds of, 60 ff.
Idealists, 56
Identity, law of, 113
Induction, 93-108, 123, 167

principle of, 103, 104, 175
Inference, logical and psy-
chological, 209
Infinity, 227 ff.
Innate, ideas and principles,

114
Introspection, 76

Judgment, 195-7

Kant, 126-41, 229
Knowledge :

by acquaintance and by

description, 70, 72-92,

170
definition of, 204 ff.
derivative, 171, 207-9
indubitable ? 8, 235
intuitive, 171, 174-85,

210 ff, 232
of future, 94 fl.
of general principles,

109-26, 131 .68
of things and of truths,

69, 72, 170, 225
of universe, 40, 2?0, 241
only of mental things ?

64 ff.
theory of, 00
philosophical, 233, 239

Laws, general, 104, 115
Leibniz,22,24,6b, 114, 148

Light, 43-5

Locke, 114

Logic, 111 £E., 144, 192,231

Mathematics, 119, 130
Matter, 18, 68

existence of, 19, 20, 22,
26-41

nature of, 42-57
Memory, 76, 180-4
Microscope, 14
Mind, 19, 81

the only reality ? 21

what is in the, 62 ff.,
154
Monad, 148
Monadism, 148
Monism, 148
Motion, laws of, 95, 99

Nature of a thing, 224
Necessity, 121

Ob jectof apprehension, 65-7
of judgment, 197

Particular, 145
Perception, 177-9, 214
Phenomena, 134
Philosophy, value of, 237-50

uncertainty of, 239-44
Physical objects, 18, 30 ff.,

53, 81, 132, 170
Plato, 142 ff.

Principles, general, 109-26
Probable opinion, 217
I ProbabiUty,96, 102,105, 114
i Proper names, 84 ff., 145
Propositions, constituents
of, 90

Qualities, 149, 159

Rationalists, 114, 134

INDEX

255

Reality, 12, 17, 24
Relations, 139, 148, 151,
159, 224-6

multiple, 194-7

sense of, 198
Resemblance, 150, 160

Self, 78 f¥.

Self -consciousness, 77

Self -evidence, 176 ff.

degrees of, 183, 215

two kinds of, 212
Sensation, 17, 132
Sense-data, 17, 23, 27, 36,
42, 73, 132, 213

certainty of, 28-30
Shapes, 15
Solipsism, 33-8
Space, 45 ff., 227 f?.

Euclidean and non-Eu-
clidean, 229

Space, physical, 47 £E.
Spinoza, 147-8
Subject, 197
Swift, 122

Thing in itself, 134
Thought, laws of, 113, 136
Time, 50 ff., 135, 100, 227 ff.
Touch, 16
Truth, 186 ff.
definition
of, 201

Uniformity of Nature, 98
Universals, 76, 81, 142-57,
231
knowledge of, 158-73,

213
not mental, 151 ff.

Verbs, 147 ff.

PLEASE DO NOT REMOVE
CARDS OR SLIPS FROM THIS POCKET

UNIVERSITY OF TORONTO LIBRARY

BD
21
R8

Russell, Bertrand Russell

The problems of
philosophy

sa